ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 ·...
Transcript of ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 ·...
![Page 1: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/1.jpg)
ECON3102-005Chapter 5: A Closed-Economy
One-Period Macroeconomic Model(Part 1)
Neha Bairoliya
Spring 2014
![Page 2: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/2.jpg)
Competitive Equilibrium
A competitive equilibrium requires that
1. The representative consumer, given his preferences and budgetconstraint, chooses c and l to maximize his utility.
2. The representative firm, given technology and the real wage, choosesNd to maximize profits.
3. All markets clear (supply=demand for each market).
4. The government satisfies its budget constraint:
G = T
![Page 3: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/3.jpg)
Competitive Equilibrium
A competitive equilibrium requires that
1. The representative consumer, given his preferences and budgetconstraint, chooses c and l to maximize his utility.
2. The representative firm, given technology and the real wage, choosesNd to maximize profits.
3. All markets clear (supply=demand for each market).
4. The government satisfies its budget constraint:
G = T
![Page 4: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/4.jpg)
Competitive Equilibrium
A competitive equilibrium requires that
1. The representative consumer, given his preferences and budgetconstraint, chooses c and l to maximize his utility.
2. The representative firm, given technology and the real wage, choosesNd to maximize profits.
3. All markets clear (supply=demand for each market).
4. The government satisfies its budget constraint:
G = T
![Page 5: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/5.jpg)
Competitive Equilibrium
A competitive equilibrium requires that
1. The representative consumer, given his preferences and budgetconstraint, chooses c and l to maximize his utility.
2. The representative firm, given technology and the real wage, choosesNd to maximize profits.
3. All markets clear (supply=demand for each market).
4. The government satisfies its budget constraint:
G = T
![Page 6: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/6.jpg)
Exogenous and Endogenous Variables
• A model takes exogenous variables, which for the purposes of theproblem at hand are determined outside the system we aremodelling, and determines values for the endogenous variables.
• In this closed-economy one-period model, the exogenous variablesare G , z ,K , and the endogenous variables are c ,Nd ,Ns ,T ,Y ,w .
• Making use of the model is running experiments to see how changesin the exogenous variables change the endogenous variables.
![Page 7: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/7.jpg)
Exogenous and Endogenous Variables
• A model takes exogenous variables, which for the purposes of theproblem at hand are determined outside the system we aremodelling, and determines values for the endogenous variables.
• In this closed-economy one-period model, the exogenous variablesare G , z ,K , and the endogenous variables are c ,Nd ,Ns ,T ,Y ,w .
• Making use of the model is running experiments to see how changesin the exogenous variables change the endogenous variables.
![Page 8: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/8.jpg)
Exogenous and Endogenous Variables
• A model takes exogenous variables, which for the purposes of theproblem at hand are determined outside the system we aremodelling, and determines values for the endogenous variables.
• In this closed-economy one-period model, the exogenous variablesare G , z ,K , and the endogenous variables are c ,Nd ,Ns ,T ,Y ,w .
• Making use of the model is running experiments to see how changesin the exogenous variables change the endogenous variables.
![Page 9: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/9.jpg)
Production Function
• Since in equilibrium labordemand should equal laborsupply, then set Ns = Nd = N.Note that this is the marketclearing condition for the labormarket.
• It follows that we can describeoutput by Y = zF (K ,N).
• Note that the maximum outputthat can be produced is Y ∗,where
Y ∗ = zF (K , h)
![Page 10: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/10.jpg)
Production Function
• Since in equilibrium labordemand should equal laborsupply, then set Ns = Nd = N.Note that this is the marketclearing condition for the labormarket.
• It follows that we can describeoutput by Y = zF (K ,N).
• Note that the maximum outputthat can be produced is Y ∗,where
Y ∗ = zF (K , h)
![Page 11: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/11.jpg)
Output as a Function of Leisure
• Recall that N = h − l . Then itmakes sense to putY = zF (K , h − l), so we canexpress output as a function ofleisure.
• If l = 0, then N = h and Y ∗ isproduced.
• If l = h, then the consumertakes all his time as leisure, andnothing is produced.
![Page 12: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/12.jpg)
Output as a Function of Leisure
• Recall that N = h − l . Then itmakes sense to putY = zF (K , h − l), so we canexpress output as a function ofleisure.
• If l = 0, then N = h and Y ∗ isproduced.
• If l = h, then the consumertakes all his time as leisure, andnothing is produced.
![Page 13: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/13.jpg)
Output as a Function of Leisure
• Recall that N = h − l . Then itmakes sense to putY = zF (K , h − l), so we canexpress output as a function ofleisure.
• If l = 0, then N = h and Y ∗ isproduced.
• If l = h, then the consumertakes all his time as leisure, andnothing is produced.
![Page 14: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/14.jpg)
Production Possibilities Frontier (PPF)
We now want to express the previous graph not as an output-leisurerelationship, but rather as a consumption-leisure relationship (the twogoods which the consumer cares about).
• Since in equilibrium Y = C + G (because of the income-expenditureidentity (aka the market clearing condition for consumption goods),then
C = Y − G
C = zF (K , h − l) − G
• So, consumption equals output minus the government expenditure.
• This means that we can take the previous graph, shift it down bysome amount G, and then get the production possibilities frontier(PPF).
![Page 15: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/15.jpg)
Production Possibilities Frontier (PPF)
We now want to express the previous graph not as an output-leisurerelationship, but rather as a consumption-leisure relationship (the twogoods which the consumer cares about).
• Since in equilibrium Y = C + G (because of the income-expenditureidentity (aka the market clearing condition for consumption goods),then
C = Y − G
C = zF (K , h − l) − G
• So, consumption equals output minus the government expenditure.
• This means that we can take the previous graph, shift it down bysome amount G, and then get the production possibilities frontier(PPF).
![Page 16: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/16.jpg)
Production Possibilities Frontier (PPF)
We now want to express the previous graph not as an output-leisurerelationship, but rather as a consumption-leisure relationship (the twogoods which the consumer cares about).
• Since in equilibrium Y = C + G (because of the income-expenditureidentity (aka the market clearing condition for consumption goods),then
C = Y − G
C = zF (K , h − l) − G
• So, consumption equals output minus the government expenditure.
• This means that we can take the previous graph, shift it down bysome amount G, and then get the production possibilities frontier(PPF).
![Page 17: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/17.jpg)
Output as a Function of Leisure
• The PPF describes thetechnological possibilities interms of consumption goodsand leisure.
• Points inside the PPF (bluearea) are feasible but notefficient.
• Points on segment AB are notfeasible (c < 0).
• Points on segment BD arefeasible.
![Page 18: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/18.jpg)
Output as a Function of Leisure
• The PPF describes thetechnological possibilities interms of consumption goodsand leisure.
• Points inside the PPF (bluearea) are feasible but notefficient.
• Points on segment AB are notfeasible (c < 0).
• Points on segment BD arefeasible.
![Page 19: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/19.jpg)
Output as a Function of Leisure
• The PPF describes thetechnological possibilities interms of consumption goodsand leisure.
• Points inside the PPF (bluearea) are feasible but notefficient.
• Points on segment AB are notfeasible (c < 0).
• Points on segment BD arefeasible.
![Page 20: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/20.jpg)
Output as a Function of Leisure
• The PPF describes thetechnological possibilities interms of consumption goodsand leisure.
• Points inside the PPF (bluearea) are feasible but notefficient.
• Points on segment AB are notfeasible (c < 0).
• Points on segment BD arefeasible.
![Page 21: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/21.jpg)
Marginal Rate of Transformation
• The negative of the slope of the PPF is also called the marginalrate of transformation; this is the rate at which one good can beconverted technologically into another.
• Call this rate the MRTl,c . In particular, note that
MRTl,c = MPN = -(slope of PPF)
![Page 22: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/22.jpg)
Marginal Rate of Transformation
• The negative of the slope of the PPF is also called the marginalrate of transformation; this is the rate at which one good can beconverted technologically into another.
• Call this rate the MRTl,c . In particular, note that
MRTl,c = MPN = -(slope of PPF)
![Page 23: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/23.jpg)
Competitive Equilibrium on Graph
• The PPF is curve FH.
• Given w , the firm chooses N tomaximize π by settingMPN = w . Hence,
N∗ = h − l∗,
Y ∗ = zF (K ,N∗),
π∗ = zF (K ,N∗) − wN∗,
maximized profit is DH.
• In equilibrium, minus the slopeof the PPF equals w ; line AD istangent to the PPF at J; hereMPN = w .
![Page 24: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/24.jpg)
Competitive Equilibrium on Graph
• The PPF is curve FH.
• Given w , the firm chooses N tomaximize π by settingMPN = w . Hence,
N∗ = h − l∗,
Y ∗ = zF (K ,N∗),
π∗ = zF (K ,N∗) − wN∗,
maximized profit is DH.
• In equilibrium, minus the slopeof the PPF equals w ; line AD istangent to the PPF at J; hereMPN = w .
![Page 25: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/25.jpg)
Competitive Equilibrium on Graph
• The PPF is curve FH.
• Given w , the firm chooses N tomaximize π by settingMPN = w . Hence,
N∗ = h − l∗,
Y ∗ = zF (K ,N∗),
π∗ = zF (K ,N∗) − wN∗,
maximized profit is DH.
• In equilibrium, minus the slopeof the PPF equals w ; line AD istangent to the PPF at J; hereMPN = w .
![Page 26: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/26.jpg)
Competitive Equilibrium on Graph
• Now let’s consider theconsumers preferences.
• Distance DB is π − G , whichequals π − T by equilibriumproperties.
• Then ADB is the consumersbudget constraint.
• Point J is the competitiveequilibrium. By consistency, c∗
is the desired consumption andhl∗ is the desired labor supply.
![Page 27: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/27.jpg)
Competitive Equilibrium on Graph
• Now let’s consider theconsumers preferences.
• Distance DB is π − G , whichequals π − T by equilibriumproperties.
• Then ADB is the consumersbudget constraint.
• Point J is the competitiveequilibrium. By consistency, c∗
is the desired consumption andhl∗ is the desired labor supply.
![Page 28: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/28.jpg)
Competitive Equilibrium on Graph
• Now let’s consider theconsumers preferences.
• Distance DB is π − G , whichequals π − T by equilibriumproperties.
• Then ADB is the consumersbudget constraint.
• Point J is the competitiveequilibrium. By consistency, c∗
is the desired consumption andhl∗ is the desired labor supply.
![Page 29: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/29.jpg)
Competitive Equilibrium on Graph
• Now let’s consider theconsumers preferences.
• Distance DB is π − G , whichequals π − T by equilibriumproperties.
• Then ADB is the consumersbudget constraint.
• Point J is the competitiveequilibrium. By consistency, c∗
is the desired consumption andhl∗ is the desired labor supply.
![Page 30: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/30.jpg)
A Necessary Condition for CompetitiveEquilibrium
MRSl,c = MRTl,c = MPN
![Page 31: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/31.jpg)
Pareto Optimal and Social Planner’s Problem
• We now have our equilibrium concept where the agents are allprice-takers and the market does all the work. But how “good” isthis market outcome?
• To answer this, the (almost) universal benchmark is that of Paretooptimality:
Definition A competitive equilibrium is Pareto optimal if there is noway to rearrange production or reallocate goods so that someone isbetter off without making someone else worse off.
![Page 32: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/32.jpg)
Pareto Optimal and Social Planner’s Problem
• We now have our equilibrium concept where the agents are allprice-takers and the market does all the work. But how “good” isthis market outcome?
• To answer this, the (almost) universal benchmark is that of Paretooptimality:
Definition A competitive equilibrium is Pareto optimal if there is noway to rearrange production or reallocate goods so that someone isbetter off without making someone else worse off.
![Page 33: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/33.jpg)
Pareto Optimal and Social Planner’s Problem
Consider now the idea of a social planner.
• He acts like a benevolent dictator whose objective is to maximizethe utility of the consumer, given the conditions of the economy.
• Since he is a dictator, he doesn’t care about prices. In particular,he is able to
1. Order the firm to hire Nd = N hours of labor and produce Y units ofoutput.
2. Order the consumer to work Ns = N hours.
3. Take an amount G of output and give the remainder to theconsumer.
![Page 34: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/34.jpg)
Pareto Optimal and Social Planner’s Problem
Consider now the idea of a social planner.
• He acts like a benevolent dictator whose objective is to maximizethe utility of the consumer, given the conditions of the economy.
• Since he is a dictator, he doesn’t care about prices. In particular,he is able to
1. Order the firm to hire Nd = N hours of labor and produce Y units ofoutput.
2. Order the consumer to work Ns = N hours.
3. Take an amount G of output and give the remainder to theconsumer.
![Page 35: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/35.jpg)
Pareto Optimal and Social Planner’s Problem
Consider now the idea of a social planner.
• He acts like a benevolent dictator whose objective is to maximizethe utility of the consumer, given the conditions of the economy.
• Since he is a dictator, he doesn’t care about prices. In particular,he is able to
1. Order the firm to hire Nd = N hours of labor and produce Y units ofoutput.
2. Order the consumer to work Ns = N hours.
3. Take an amount G of output and give the remainder to theconsumer.
![Page 36: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/36.jpg)
Pareto Optimal and Social Planner’s Problem
Consider now the idea of a social planner.
• He acts like a benevolent dictator whose objective is to maximizethe utility of the consumer, given the conditions of the economy.
• Since he is a dictator, he doesn’t care about prices. In particular,he is able to
1. Order the firm to hire Nd = N hours of labor and produce Y units ofoutput.
2. Order the consumer to work Ns = N hours.
3. Take an amount G of output and give the remainder to theconsumer.
![Page 37: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/37.jpg)
Pareto Optimal and Social Planner’s Problem
Consider now the idea of a social planner.
• He acts like a benevolent dictator whose objective is to maximizethe utility of the consumer, given the conditions of the economy.
• Since he is a dictator, he doesn’t care about prices. In particular,he is able to
1. Order the firm to hire Nd = N hours of labor and produce Y units ofoutput.
2. Order the consumer to work Ns = N hours.
3. Take an amount G of output and give the remainder to theconsumer.
![Page 38: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/38.jpg)
Pareto Optimal and Social Planner’s Problem
Hence the planners problem is to choose c and l that, given technologicalconstraints, maximize the utility of the consumer.
• Formally, he solves:maxc,l
U(c , l)
subject to c = zF (K , h − l) − G
c ≥ 0
0 ≤ l ≤ h
![Page 39: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/39.jpg)
Pareto Optimal and Social Planner’s Problem
• The solution to the socialplanner’s problem is ParetoOptimal.
• The Pareto optimum is point B,where I1 is tangent to the PPF.
• This is similar to our previousproblem, but we don’t get toworry about the budgetconstraint.
![Page 40: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/40.jpg)
Pareto Optimal and Social Planner’s Problem
• The solution to the socialplanner’s problem is ParetoOptimal.
• The Pareto optimum is point B,where I1 is tangent to the PPF.
• This is similar to our previousproblem, but we don’t get toworry about the budgetconstraint.
![Page 41: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/41.jpg)
Pareto Optimal and Social Planner’s Problem
• The solution to the socialplanner’s problem is ParetoOptimal.
• The Pareto optimum is point B,where I1 is tangent to the PPF.
• This is similar to our previousproblem, but we don’t get toworry about the budgetconstraint.
![Page 42: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/42.jpg)
Pareto Optimal and Social Planner’s Problem
From the figure note that
• The slope of the indifferencecurve is MRSl,c
• The slope of the PPF is givenby MRTl,c
• The slope of the PPF is alsogiven by MPN
• Pareto optimality satisfies MRSl,c = MRTl,c = MPN .
![Page 43: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/43.jpg)
Pareto Optimal and Social Planner’s Problem
From the figure note that
• The slope of the indifferencecurve is MRSl,c
• The slope of the PPF is givenby MRTl,c
• The slope of the PPF is alsogiven by MPN
• Pareto optimality satisfies MRSl,c = MRTl,c = MPN .
![Page 44: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/44.jpg)
Pareto Optimal and Social Planner’s Problem
From the figure note that
• The slope of the indifferencecurve is MRSl,c
• The slope of the PPF is givenby MRTl,c
• The slope of the PPF is alsogiven by MPN
• Pareto optimality satisfies MRSl,c = MRTl,c = MPN .
![Page 45: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/45.jpg)
Pareto Optimal and Social Planner’s Problem
From the figure note that
• The slope of the indifferencecurve is MRSl,c
• The slope of the PPF is givenby MRTl,c
• The slope of the PPF is alsogiven by MPN
• Pareto optimality satisfies MRSl,c = MRTl,c = MPN .
![Page 46: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/46.jpg)
CE and Pareto Optimum
• In this model, the competitive equilibrium and the Pareto optimumare identical, as both satisfies
MRSl,c = MRTl,c = MPN
• We come to the two of the most important theorems in Economics:
• Theorem (The First Fundamental Theorem of WelfareEconomics) Under certain conditions, a competitive equilibrium isPareto optimal.
• Theorem (The Second Fundamental Theorem of WelfareEconomics) Under certain conditions, a Pareto optimal allocationcan be established as a competitive equilibrium.
• Free market economies tend to produce socially efficient economicoutcomes.
![Page 47: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/47.jpg)
CE and Pareto Optimum
• In this model, the competitive equilibrium and the Pareto optimumare identical, as both satisfies
MRSl,c = MRTl,c = MPN
• We come to the two of the most important theorems in Economics:
• Theorem (The First Fundamental Theorem of WelfareEconomics) Under certain conditions, a competitive equilibrium isPareto optimal.
• Theorem (The Second Fundamental Theorem of WelfareEconomics) Under certain conditions, a Pareto optimal allocationcan be established as a competitive equilibrium.
• Free market economies tend to produce socially efficient economicoutcomes.
![Page 48: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/48.jpg)
CE and Pareto Optimum
• In this model, the competitive equilibrium and the Pareto optimumare identical, as both satisfies
MRSl,c = MRTl,c = MPN
• We come to the two of the most important theorems in Economics:
• Theorem (The First Fundamental Theorem of WelfareEconomics) Under certain conditions, a competitive equilibrium isPareto optimal.
• Theorem (The Second Fundamental Theorem of WelfareEconomics) Under certain conditions, a Pareto optimal allocationcan be established as a competitive equilibrium.
• Free market economies tend to produce socially efficient economicoutcomes.
![Page 49: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/49.jpg)
CE and Pareto Optimum
• In this model, the competitive equilibrium and the Pareto optimumare identical, as both satisfies
MRSl,c = MRTl,c = MPN
• We come to the two of the most important theorems in Economics:
• Theorem (The First Fundamental Theorem of WelfareEconomics) Under certain conditions, a competitive equilibrium isPareto optimal.
• Theorem (The Second Fundamental Theorem of WelfareEconomics) Under certain conditions, a Pareto optimal allocationcan be established as a competitive equilibrium.
• Free market economies tend to produce socially efficient economicoutcomes.
![Page 50: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/50.jpg)
CE and Pareto Optimum
• In this model, the competitive equilibrium and the Pareto optimumare identical, as both satisfies
MRSl,c = MRTl,c = MPN
• We come to the two of the most important theorems in Economics:
• Theorem (The First Fundamental Theorem of WelfareEconomics) Under certain conditions, a competitive equilibrium isPareto optimal.
• Theorem (The Second Fundamental Theorem of WelfareEconomics) Under certain conditions, a Pareto optimal allocationcan be established as a competitive equilibrium.
• Free market economies tend to produce socially efficient economicoutcomes.
![Page 51: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/51.jpg)
Sources of Social Inefficiency
• The previous theorems sound nice, but do they always hold? Moreimportantly, when do they not hold?
• This motivates a discussion about the sources of socialinefficiencies.
• We have 3 factors that violate the equivalence between the first andsecond theorem.
1. Externalities
2. The presence of market power
3. Distorting taxes
![Page 52: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/52.jpg)
Sources of Social Inefficiency
• The previous theorems sound nice, but do they always hold? Moreimportantly, when do they not hold?
• This motivates a discussion about the sources of socialinefficiencies.
• We have 3 factors that violate the equivalence between the first andsecond theorem.
1. Externalities
2. The presence of market power
3. Distorting taxes
![Page 53: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/53.jpg)
Sources of Social Inefficiency
• The previous theorems sound nice, but do they always hold? Moreimportantly, when do they not hold?
• This motivates a discussion about the sources of socialinefficiencies.
• We have 3 factors that violate the equivalence between the first andsecond theorem.
1. Externalities
2. The presence of market power
3. Distorting taxes
![Page 54: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/54.jpg)
Sources of Social Inefficiency
• The previous theorems sound nice, but do they always hold? Moreimportantly, when do they not hold?
• This motivates a discussion about the sources of socialinefficiencies.
• We have 3 factors that violate the equivalence between the first andsecond theorem.
1. Externalities
2. The presence of market power
3. Distorting taxes
![Page 55: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/55.jpg)
Sources of Social Inefficiency
• The previous theorems sound nice, but do they always hold? Moreimportantly, when do they not hold?
• This motivates a discussion about the sources of socialinefficiencies.
• We have 3 factors that violate the equivalence between the first andsecond theorem.
1. Externalities
2. The presence of market power
3. Distorting taxes
![Page 56: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/56.jpg)
Sources of Social Inefficiency
• The previous theorems sound nice, but do they always hold? Moreimportantly, when do they not hold?
• This motivates a discussion about the sources of socialinefficiencies.
• We have 3 factors that violate the equivalence between the first andsecond theorem.
1. Externalities
2. The presence of market power
3. Distorting taxes
![Page 57: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/57.jpg)
Externalities
• Negative externalities cause overproduction of the good.
• Positive externalities cause underproduction of the good.
• Hence, the socially efficient outcome is not reached. A competitiveequilibrium is not Pareto optimal.
![Page 58: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/58.jpg)
Externalities
• Negative externalities cause overproduction of the good.
• Positive externalities cause underproduction of the good.
• Hence, the socially efficient outcome is not reached. A competitiveequilibrium is not Pareto optimal.
![Page 59: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/59.jpg)
Externalities
• Negative externalities cause overproduction of the good.
• Positive externalities cause underproduction of the good.
• Hence, the socially efficient outcome is not reached. A competitiveequilibrium is not Pareto optimal.
![Page 60: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/60.jpg)
Market Power
• As you remember from 1101, monopoly power leads tounderproduction relative to the social optimum:
• A competitive equilibrium is not Pareto optimal.
![Page 61: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/61.jpg)
Market Power
• As you remember from 1101, monopoly power leads tounderproduction relative to the social optimum:
• A competitive equilibrium is not Pareto optimal.
![Page 62: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/62.jpg)
Distorting Taxes
• Assume that there is a proportional tax over wage income. Then thebudget constraint is
c = w(1 − t)Ns + π − T , t < 1
• Since optimality for the consumer requires equality between themarginal rate of substitution and the price ratio, we have that
w(1 − t) = MRSl,c
• But the firm optimizes when MPN = w , so
MRSl,c < MPN = MRTl,c
• And the equivalence condition breaks down.
![Page 63: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/63.jpg)
Distorting Taxes
• Assume that there is a proportional tax over wage income. Then thebudget constraint is
c = w(1 − t)Ns + π − T , t < 1
• Since optimality for the consumer requires equality between themarginal rate of substitution and the price ratio, we have that
w(1 − t) = MRSl,c
• But the firm optimizes when MPN = w , so
MRSl,c < MPN = MRTl,c
• And the equivalence condition breaks down.
![Page 64: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/64.jpg)
Distorting Taxes
• Assume that there is a proportional tax over wage income. Then thebudget constraint is
c = w(1 − t)Ns + π − T , t < 1
• Since optimality for the consumer requires equality between themarginal rate of substitution and the price ratio, we have that
w(1 − t) = MRSl,c
• But the firm optimizes when MPN = w , so
MRSl,c < MPN = MRTl,c
• And the equivalence condition breaks down.
![Page 65: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/65.jpg)
Distorting Taxes
• Assume that there is a proportional tax over wage income. Then thebudget constraint is
c = w(1 − t)Ns + π − T , t < 1
• Since optimality for the consumer requires equality between themarginal rate of substitution and the price ratio, we have that
w(1 − t) = MRSl,c
• But the firm optimizes when MPN = w , so
MRSl,c < MPN = MRTl,c
• And the equivalence condition breaks down.
![Page 66: ECON3102-005 Chapter 5: A Closed-Economy One-Period Macroeconomic Model … · 2017-10-26 · One-Period Macroeconomic Model (Part 1) Neha Bairoliya Spring 2014. Competitive Equilibrium](https://reader030.fdocuments.us/reader030/viewer/2022041023/5ed60ce249af592c00577029/html5/thumbnails/66.jpg)
Solving the CE
• To avoid dealing with prices we will use the equivalence betweencompetitive equilibrium and Pareto optimal allocations. Thus, thesolution to the planners problem is our competitive equilibrium.