LECTURE 18 - shapiromh.com · Test will cover lecture 11 through 20 ... • Review sessions next...

LECTURE 18 28 March 2013

1Thursday, March 28, 13

ANNOUNCEMENTS

• HW 7 due tomorrow

• Supply worksheet for recitation next week

• Extra notes on consumer theory (why MRS = OC) on my website shapiromh.weebly.com


MIDTERM 2

• Midterm 2 in 2 weeks (Monday 8th from 7:30 - 8:30 PM)

• If you need to take the makeup email [email protected] by Monday the 1st at 4PM

• Start reviewing! Test will cover lecture 11 through 20 (externalities through next week) and readings 4-6

• Review sessions next Wednesday from 4-5:30 and 6-7:30

• Sample midterms with solutions available on Moodle

• Extra Office hours next week, Thursday, the 4th: 10:00 AM - Noon


mailto:[email protected]

mailto:[email protected]

INCOME AND SUBSTITUTION EFFECTS

• Economists have special names for the two effects from price changes on demand:

• Substitution effect is the effect of the change in opportunity cost, holding income fixed (we do this by holding utility spending power fixed, i.e. how much utility I can get)

• Income effect is the effect of the change income, holding price ratio (opportunity cost) fixed

• The total effect = substitution effect + income effect


TOTAL EFFECT OF PRICES

• We start with the blue optimal consumption point: consume 6 wine, 3 cheese

• Price of cheese falls to $2

• The optimal consumption is the pink point with consumption of 7 wine, 5 cheese

• Total change is the movement from the blue to pink dot

• 1 unit increase in wine

• 2 unit increase in cheese

0123456789

10

0 1 2 3 4 5 6 7 8 9 10

1112

11121314

13141516

Cheese

Wine

New BCOld BC

Donald’s Consumption


SUBSTITUTION EFFECT

• Remember for the substitution effect you want to fix utility (so stay on same IC) but with the same opportunity costs

• So we create a budget line (orange) that is parallel to the new budget line (keep opportunity cost fixed to the new level) but touches the old indifference curve once

• On the orange line, Donald will choose to consume a bundle that gives exactly the same utility as the original utility

• He consumes 4 cheese and 5 wine

• The movement from the blue to the orange is the substitution effect -- it only captures the effect of opportunity cost change

• Wine changed by -1 and cheese increased by 1

0123456789

10

0 1 2 3 4 5 6 7 8 9 10

1112

11121314

13141516

Cheese

Wine

New BCOld BC



INCOME EFFECT

• Once you have figured out the substitution effect, the income effect follows from total effect - substitution effect

• It is the change from the orange bundle to the pink bundle

• Because of the income effect wine spending increased by 2 and cheese by 1

0123456789

10

0 1 2 3 4 5 6 7 8 9 10

1112

11121314

13141516

Cheese

Wine

New BCOld BC



PATTERNS IN SUBSTITUTION AND INCOME EFFECTS

• When price falls, the substitution effect suggests: buy more of that thing because the opportunity cost fell

• The income effect is positive for normal goods and negative for inferior

• If the good is normal, then substitution and income effect work in the same direction as we see with cheese

• Why did the substitution effect cause wine demand to decrease?

• Relative price rose

• OC was 1/2 cheese but rose to 1

Price of cheese falls from $4 to $2



Effect on Wine

Effect on Cheese

Substitution -1 demand +1 demand

Income +2 demand +1 demand

Total +1 demand +2 demand


APPLICATION: LABOR MARKETS

• Important application is to labor supply (how much we decide to work)

• When price (wage) increases, we have higher income, but what is the cost to more work?

• We love leisure! And we can work or we can enjoy leisure

• Leisure is a normal good (we want more free time with the more money we have so we can spend it)

Aguiar and Hurst, 2007



• Income Effect on leisure

• Our income is rising with wage

• Income effect tells us we want to work less (have more leisure) the more we earn

• Substitution Effect

• How costly is leisure (not working)?

• Whatever wage is; the wage is the opportunity cost of leisure

• So rising wage increases the opportunity cost of leisure

• Substitution effect indicates we should want to work more because leisure is costly



• So which effect dominates over time

• Do you think we are working more (substitution effect dominates) or less and enjoying more leisure (income effect dominates)?

• It seems that with time and growing income, time spent working has decreased so income effect has dominated

• Or is the cost of working becoming higher?

• Is leisure more enjoyable or valuable now than 50 years ago?


REVISITING TOM AND CRUSOE


CRUSOE’S GAIN FROM TRADE

• Recall this picture from trade between Crusoe and Tom

• We were unable to justify the optimal consumption in autarky (purple dot) and in trade (red dot)

• So add preferences!

• In autarky, what is Crusoe’s budget constraint?

• The PPF limits his consumption

• It must be that the purple dot is the consumption bundle that maximizes utility of all bundles in the consumption set

Lobster

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

Crusoe PPF

22

24

22 24

Melon

Trade consumption

Trade production

Crusoe Production and ConsumptionCrusoe Production and ConsumptionCrusoe Production and ConsumptionProduce Consume

Autarky 12 L, 4 M 12 L, 4 MTrade 24 L, 0 M 12 L, 12 M

Autarky

IC 1

IC 2


CRUSOE’S GAIN FROM TRADE• Remember the world price was 1 melon for 1

lobster

• What is Crusoe’s budget constraint in trade when he specializes in lobster?

• The light blue line

• Think of the extremes on the BC: one is keep the lobster I make, one is sell all my lobster and get 24 melons

• The red dot maximizes utility of all bundles in the new set of things that are affordable

• So what trade really did was expand Crusoe’s “affordable goods”!

• Additionally, he is on a higher IC now so his utility improved after trade

Lobster

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

Crusoe PPF

22

24

22 24

Melon

Trade consumption

Trade production

Crusoe Production and ConsumptionCrusoe Production and ConsumptionCrusoe Production and ConsumptionProduce Consume


Autarky

BC, trade

IC 1

IC 2


TOM’S GAIN FROM TRADE

• The same analysis can be done for Tom

• Opening to trade allows Tom to expand his set of affordable goods

• Now he can consume a bundle (red dot) that gives him more utility than in autarky (purple dot)

Lobster

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

Tom PPF

22

24

22 24

Melon

Trade consumption

Trade production

Tom Production and ConsumptionTom Production and ConsumptionTom Production and ConsumptionProduce Consume


Autarky

IC 1

IC 2


SUMMARY 1

• Notice all of the concepts embodied in the trade model with Crusoe and Tom

• Production possibilities

• Consumer choice

• Specialization in trade

• Gains from trade

• Market Clearing (supply = demand) in lobster and melons

Lobster

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

Tom PPF

22

24

22 24

Melon

Trade consumption

Trade production

Tom Production and ConsumptionTom Production and ConsumptionTom Production and ConsumptionProduce Consume


Autarky

IC 1

IC 2


SUMMARY 2

• Budget issues limit what consumers can consume

• From that budget constrained sets, consumers choose consumption bundles that maximize their utility

• A utility function is something that represents a consumer’s preference for different bundles by placing a numerical value (utils) on different quantities of goods

• Indifference curves represent different bundles that yield the same utility

• The income and substitution effects break down the effect on demand of real income changes and opportunity cost changes respectively following a price change


TOPIC 13Production


BIG PICTURE

• How can we model a more realistic picture of firm production and costs?

• How do different types of production functions and costs affect firm supply?

• How does firm supply change in the short and the long-run in a competitive market?

• In a competitive how can we add over individual firms to create a market-wide aggregate supply?


INTRODUCTION TO FIRMS


COMPLICATING PRODUCERS

• In MacLand, like our consumers, our producers were simple

• Each could produce or not produce

• Each would produce if price was higher than some associated cost

• In reality firms produce far more than 1 unit and costs vary with the amount that produce

FoxConn produces far more than 1 unit


A MORE REALISTIC PRODUCER

• Suppose a new producer is in town, S11 (Lucas), and produces Diet Coke

• She has a very sophisticated operation that can produce more than one coke but faces more complex costs

1. Fixed costs - costs that are the same regardless of the amount she produces

2. Variable costs - costs that vary with the amount she produces

• Fixed costs include things like CEO salary, electricity bill, factor rent that must be paid to be open but do not vary much with quantity

• Variable costs include labor, inputs (materials) that certainly change with the amount produces


DIET COKE PRODUCTION

• S11 needs to ay $4 in fixed costs (factory rent)

• In variable costs, she pays $2 an hour to labor and $1 per pint of aspartame needed for each Diet Coke

• The table to the right shows how much labor is required to produce each unit (we assume how much)

Quant Labor Hours

Labor Cost

Material Cost

Variable Cost

0 0.0 $0 $0 $0

1 0.5 $1 $1 $2

2 2.0 $4 $2 $6

3 4.5 $9 $3 $12

4 8.0 $16 $4 $20


VARIABLE COSTS

• Variable costs here are the sum of labor costs and material (aspartame) costs

• You can check that total variable cost (VC) = Q + Q2

• Notice labor costs are equal to Q2

• Material costs are equal to Q

Quant Labor Hours

Labor Cost

Material Cost

Variable Cost

0 0.0 $0 $0 $0

1 0.5 $1 $1 $2

2 2.0 $4 $2 $6

3 4.5 $9 $3 $12

4 8.0 $16 $4 $20


DIMINISHING RETURNS

• This type of cost structure shows diminishing marginal returns

• The idea is similar to increasing returns to scale or diminishing rate of substitution

• Diminishing marginal returns in general means the output I get from adding more input decreases with the amount of input

• Looking at the chart, we see it only takes .5 labor to produce the first diet coke

• To produce the second requires 1.5 more and then 2.5 on top of that, etc.

• Diminishing marginal returns to labor: the return I get from adding labor to producing Diet Cokes decreases with the amount of labor I have

• One way to think about it is like picking low hanging fruit; do the easiest jobs first


TOTAL COSTS

• We now know variable costs for producing each Diet Coke and fixed costs are ... fixed at $4

• Total costs are the sum of fixed and variable costs TC = VC + FC

• Average fixed costs (AFC) = FC / Q; this should be falling the more we produce, why?

• Average variable costs (AVC) = VC / Q

Quant Fixed Cost (FC)

Variable Cost (VC)

Total Cost (TC)

0 $4 $0 $4

1 $4 $2 $6

2 $4 $6 $10

3 $4 $12 $16

4 $4 $20 $24


AVERAGE COSTS

• Notice that ATC = AVC + AFC (just divide TC = VC + FC by Q)

• These average costs will be important later

• In general, economists are most concerned about the margin

• Marginal costs (MC) - change in total cost from increasing output by one unit

• How did I derive these MCs?

Q AFC AVC ATC MC

0 -- -- -- --

1 $4.00 $2.00 $6.00 $3.00

2 $2.00 $3.00 $5.00 $5.00

3 $1.33 $4.00 $5.33 $7.00

4 $1.00 $5.00 $6.00 $9.00


MARGINAL COSTS• What is the marginal cost between Q= 0

and 1?

• Total cost changes from 4 to 6

• So marginal cost is 2

• MC between Q=1 and Q=2 is 4 and so on

• To find the MC at 1 we need to use a midpoint formula

• E.g. MC at 1 is the midpoint of the MC between Q=0 and Q=1 and MC between Q=1 and Q=2

• MC at 1 is then $3

• Check that MC at Q=2 is $5

Quant Fixed Cost (FC)

Variable Cost (VC)

Total Cost (TC)

0 $4 $0 $4

1 $4 $2 $6

2 $4 $6 $10

3 $4 $12 $16

4 $4 $20 $24


GENERAL COST FORMULAS

• We can also sacrifice intuition and propose some general cost formulas

• In general a firm’s total cost might look like TC = aQ2 + bQ + c

• When total cost looks like that MC = 2aQ +b (should be clear to those with calculus backgrounds, otherwise we can memorize the formula)

• a,b,c are called parameters of the cost function; firms can have very similar cost functions but still be very different because of differences in these parameters


GENERAL COST FORMULAS

• In our case, remember that VC = Q2 + Q and FC = 4 so TC = Q2 + Q + 4

• So our firm fits in into the general cost formula with a=1, b=1, c=4

• What is marginal cost here?

• General formula is 2aQ +b

• So MC = 2Q + 1


PARAMETERS OF COST

• The parameters in TC = aQ2 + bQ + c have a natural interpretation

• c is a fixed cost (notice it doesn’t grow with quantity); for Airbus researching planes this is huge $16 billion, for Diet Coke, the fixed costs are probably smaller

• b is a variable cost (notice it grows proportional to quantity)

• a does not have a natural interpretation and in most cases will be 0

• If a>0, marginal costs are increasing with Q (this is equivalent to saying there are diminishing marginal returns); can you check this in the formula?

• We have a numerical story of S11, what do we care about graphically?


GRAPHING COST STRUCTURE

• It will turn out that the average (except fixed, that’s boring) and marginal costs are most important

• We will talk about the impact on supply later

• For now, be able to graph AVC, MC, ATC

S11 Costs

00

1

Quantity

$

1 2 43 5

2345678910

MC

ATC

AVC


• Notice that at a quantity of 2, ATC switches from decreasing to increasing

• When ATC is falling (Q<2), we have increasing returns to scale (think of lower cost as a measure of higher productivity to relate it to our Crusoe Tom discussion)

• IRS is also known as economies of scale

• For Q>2, ATC is rising: this is decreasing returns to scale or diseconomies of scale

S11 Costs

00

1

Quantity

$

1 2 43 5

2345678910

MC

ATC

AVC

INTERPRETATION OF AVERAGE COSTS


• Is anything else interesting?

• The MC curve seems to cross at the point of change in direction of ATC

• For Q<2, MC < ATC and ATC falling

• For Q>2, MC > ATC and ATC rising

• For Q = 2, MC = ATC and ATC is at its minimum

S11 Costs

00

1

Quantity

$

1 2 43 5

2345678910

MC

ATC

AVC

INTERPRETATION OF AVERAGE COSTS


CONSTANT RETURNS TO SCALE

• For Lucas (S11), we saw that for certain quantities he enjoyed increasing returns to scale at others decreasing returns to scale

• Some producers have constant returns to scale (CRS) production functions

• CRS: If all inputs increase by the same factor, then costs will rise by that factor (and production will rise by that factor)

• Introduce S12 (Jabba) who paints houses in his free time and has production with constant returns to scale


CONSTANT RETURNS TO SCALE

Quantity Total Cost ATC0 0 --1 5 52 10 53 15 54 20 5

S12 (Jabba)’s Cost Structure

• Remember in general: TC = aQ2 + bQ + c

• Here a=0, b=5, c=0

S12 Costs

00

1

Quantity

$

1 2 43 5

2345678910

ATC = MC

Notice in this case MC is constant and = ATC


ECONOMIES OF SCALE

• Finally S13 (Bill) will enjoy increasing returns to scale, or economies of scale, over his entire production (versus for some Q like with S11)

• Suppose he has FC = 8 and constant marginal cost MC =2

• This second assumption is a major difference from S11 who had increasing marginal cost

• So his total cost is TC =2Q + 8

• Since ATC = TC / Q, ATC = 2 + 8/Q

• How will this type of production look?


ECONOMIES OF SCALE (OVER ALL Q)

Quantity Total Cost ATC0 8 --1 10 102 12 63 14 4.66666674 16 4... ... ...8 24 3

S13 (Bill)’s Cost Structure S13 Costs

00

1

Quantity

$

1 2 43 5

2345678910

MC

ATC

Notice ATC falls over the whole range of Q

TC =2Q + 8 38Thursday, March 28, 13

APPLICATION: EOS FIRMS

• Economies of scale play an important role in many industries; examples?

• Pharmaceuticals - there is a huge one-off fixed cost for developing a drug but small cost in producing a pill

• Software - big research cost (maybe not for Windows...) and small marginal cost (or basically 0 with internet distribution)

• Big airlines - Airbus spent $16 BILLION developing their A 380 jumbojet (all before the first income on the plane)


APPLICATION: EOS FIRMS

• Discount retailing and Wal-Mart:

• Wal-Mart lowers average total costs by expanding its operation while minimizing fixed costs (like setting up distribution centers)

• Wal-Mart packs its store closely to take advantage of economies of density, lower transit costs, for example, by having stores in close proximity

• Can look at Wal-Mart’s expansion on Professor’s Holmes website or here

• In industries with high fixed costs there are usually few firms (we will talk about why soon)

• But we want to focus on perfectly competitive markets for now where an individual firm is too insignificant to affect price


http://www.econ.umn.edu/~holmes/papers/Wal1962-2004_nov_05.wmv

http://www.econ.umn.edu/~holmes/papers/Wal1962-2004_nov_05.wmv

http://projects.flowingdata.com/walmart/

http://projects.flowingdata.com/walmart/

LECTURE 18 - shapiromh.com · Test will cover lecture 11 through 20 ... • Review sessions next...

Documents

Transcript of LECTURE 18 - shapiromh.com · Test will cover lecture 11 through 20 ... • Review sessions next...