Fundamental Economic Concepts
Chapter 2
Fundamental Economic Concepts
Demand, Supply, and Equilibrium Review Total, Average, and Marginal Analysis Finding the Optimum Point Present Value, Discounting & Net Present
Value Risk and Expected Value Probability Distributions Standard Deviation & Coefficient of Variation Normal Distributions and using the z-value The Relationship Between Risk & Return
Law of Demand
A decrease in the price of a good, all other things held constant, will cause an increase in the quantity demanded of the good.
An increase in the price of a good, all other things held constant, will cause a decrease in the quantity demanded of the good.
Change in Quantity Demanded
Quantity
Price
P0
Q0
P1
Q1
An increase in price causes a decrease in quantity demanded.
Change in Quantity Demanded
Quantity
Price
P0
Q0
P1
Q1
A decrease in price causes an increase in quantity demanded.
Demand Curves Individual Demand
Curve the greatest quantity of a good demanded at each price the consumers are willing to buy, holding other influences constant
$/Q
Q /time unit
$5
20
The Market Demand Curve is the horizontal sum of the individual demand curves.
The Demand
Function includes all variables that influence the quantity demanded
4 3 7
Sam + Diane = Market
Q = f( P, Ps, Pc, Y, N PE) - + - ? + +
P is price of the goodPS is the price of substitute goodsPC is the price of complementary goodsY is income, N is population, PE is the expected future price
Determinants of the Quantity DemandedDeterminants of the Quantity Demanded
i. price, P
ii. price of substitute goods, Ps
iii. price of complementary goods, Pc
iv. income, Y
v. advertising, A
vi. advertising by competitors, Ac
vii. size of population, N,
viii. expected future prices, Pe
xi. adjustment time period, Ta
x. taxes or subsidies, T/S
The list of variables that could likely affect the quantity demand varies for different industries and products.
The ones on the left are tend to be significant.
Change in Demand
Quantity
Price
P0
Q0 Q1
An increase in demand refers to a rightward shift in the market demand curve.
Change in Demand
Quantity
Price
P0
Q1 Q0
A decrease in demand refers to a leftward shift in the market demand curve.
Figure 2.3 Shifts in Demand
Law of Supply
A decrease in the price of a good, all other things held constant, will cause a decrease in the quantity supplied of the good.
An increase in the price of a good, all other things held constant, will cause an increase in the quantity supplied of the good.
Change in Quantity Supplied
Quantity
Price
P1
Q1
P0
Q0
A decrease in price causes a decrease in quantity supplied.
Change in Quantity Supplied
Quantity
Price
P0
Q0
P1
Q1
An increase in price causes an increase in quantity supplied.
Supply Curves
Firm Supply Curve - the greatest quantity of a good supplied at each price the firm is profitably able to supply, holding other things constant.
$/Q
Q/time unit
The Market Supply Curve is the horizontal sum of the firm supply curves.
The Supply
Function includes all variables that influence the quantity supplied
4 3 7
Acme Inc. + Universal Ltd. = Market
Q = g( P, PI, RC, T, T/S)Q = g( P, PI, RC, T, T/S) + - - + ?
i. price, P
ii. input prices, PI, e.g., sheet metal
iii. Price of unused substitute inputs, PUI, such as fiberglass
iv. technological improvements, T
v. entry or exit of other auto sellers, EE
vi. Accidental supply interruptions from fires, floods, etc., F
vii. Costs of regulatory compliance, RC
viii. Expected future changes in price, PE
ix. Adjustment time period, TA
x. taxes or subsidies, T/S
Note: Anything that shifts supply can be included and varies for different industries or products.
Determinants of the Supply Function
Change in Supply
Quantity
Price
P0
Q1Q0
An increase in supply refers to a rightward shift in the market supply curve.
Change in Supply
Quantity
Price
P0
Q1 Q0
A decrease in supply refers to a leftward shift in the market supply curve.
Market Equilibrium
Market equilibrium is determined at the intersection of the market demand curve and the market supply curve.
The equilibrium price causes quantity demanded to be equal to quantity supplied.
Equilibrium: No Tendency to
Change
Superimpose demand and supply
If No Excess Demand and No Excess Supply . . .
Then no tendency to change at the equilibrium price, Pe D
S
Pe
Q
P
Willing& Ablein cross-hatched
Dynamics of Supply and DemandDynamics of Supply and Demand If quantity demanded is greater than quantity
supplied at a price, prices tend to rise. The larger is the difference between quantity
supplied and demanded at a price, the greater is the pressure for prices to change.
When the quantity demanded and supplied at a price are equal at a price, prices have no tendency to change.
Equilibrium Price Movements Suppose there is an
increase in income this year and assume the good is a “normal” good
Does Demand or Supply Shift?
Suppose wages rose, what then?
D
S
e1
P
Q
P1
Comparative Statics& the supply-demand model
Suppose that demand Shifts to D’ later this fall…
We expect prices to rise
We expect quantity to rise as wellD
S
e1
P
Q
D’e2
Market Equilibrium
Quantity
Price
P0
Q0
D0 S0
Q1
P1
D1
An increase in demand will cause the market equilibrium price and quantity to increase.
Market Equilibrium
Quantity
Price
P1
Q1
S0
Q0
P0
D0D1
A decrease in demand will cause the market equilibrium price and quantity to decrease.
Market Equilibrium
Quantity
Price
P0
Q0
D0 S0
Q1
P1
An increase in supply will cause the market equilibrium price to decrease and quantity to increase.
S1
Market Equilibrium
Quantity
Price
P1
Q1
D0
Q0
P0
A decrease in supply will cause the market equilibrium price to increase and quantity to decrease.
S1 S0
Break Decisions Into Smaller Units: How Much to Produce ?
Graph of output and profit
Possible Rule: Expand output until
profits turn down But problem of
local maxima vs. global maximum
quantity B
MAX
GLOBALMAX
profit
A
Average Profit = Profit / Q
Slope of ray from the origin Rise / Run Profit / Q = average profit
Maximizing average profit doesn’t maximize total profit
MAX
C
B
profits
Q
PROFITS
quantity
Marginal Profits = /Q
Q1 is breakeven (zero profit) maximum marginal profits occur at the
inflection point (Q2) Max average profit at Q3 Max total profit at Q4 where marginal
profit is zero So the best place to produce is where
marginal profits = 0.
FIGURE 2.8 Total, Average, and Marginal Profit Functions
Present Value Present value recognizes that a dollar received
in the future is worth less than a dollar in hand today.
To compare monies in the future with today, the future dollars must be discounted by a present value interest factor, PVIF=1/(1+i), where i is the interest compensation for postponing receiving cash one period.
For dollars received in n periods, the discount factor is PVIFn =[1/(1+i)]n
Net Present Value (NPV) Most business decisions are long term
capital budgeting, product assortment, etc.
Objective: Maximize the present value of profits NPV = PV of future returns - Initial Outlay NPV = t=0 NCFt / ( 1 + rt )t
where NCFt is the net cash flow in period t
NPV Rule: Do all projects that have positive net present values. By doing this, the manager maximizes shareholder wealth.
Good projects tend to have: 1. high expected future net cash flows
2. low initial outlays
3. low rates of discount
Sources of Positive NPVs
1. Brand preferences for established brands
2. Ownership control over distribution
3. Patent control over products or techniques
4. Exclusive ownership over natural resources
5. Inability of new firms to acquire factors of production
6. Superior access to financial resources
7. Economies of large scale or size from either:
a. Capital intensive processes, or
b. High start up costs
Appendix 2ADifferential Calculus Techniques in
Management
A function with one decision variable, X, can be written as Y = f(X)
The marginal value of Y, with a small increase of X, is My = Y/X
For a very small change in X, the derivative is written:
dY/dX = limit Y/XX B
Marginal = Slope = Derivative
The slope of line C-D is Y/X
The marginal at point C is My is Y/X
The slope at point C is the rise (Y) over the run (X)
The derivative at point C is also this slope
X
C
DY
Y
X
Finding the maximum flying range forthe Stealth Bomber is an optimization problem.
Calculus teaches that when the first derivative is zero, the solution is at an optimum.
The original Stealth Bomber study showed that a controversial flying V-wing design optimized the bomber's range, but the original researchers failed to find that their solution in fact minimized the range.
It is critical that managers make decision that maximize, not minimize, profit potential!
Quick Differentiation Review
Constant Y = c dY/dX = 0 Y = 5
Functions dY/dX = 0
A Line Y = c•X dY/dX = c Y = 5•X
dY/dX = 5
Power Y = cXb dY/dX = b•c•X b-1 Y = 5•X2
Functions dY/dX = 10•X
Name Function Derivative Example
Sum of Y = G(X) + H(X) dY/dX = dG/dX + dH/dX
Functions
example Y = 5•X + 5•X2 dY/dX = 5 + 10•X
Product of Y = G(X)•H(X)
Two Functions dY/dX = (dG/dX)H + (dH/dX)G
example Y = (5•X)(5•X2 )
dY/dX = 5(5•X2 ) + (10•X)(5•X) = 75•X2
Quick Differentiation Review
Quotient of Two Y = G(X) / H(X) Functions
dY/dX = (dG/dX)•H - (dH/dX)•G H2
Y = (5•X) / (5•X2) dY/dX = 5(5•X2) -(10•X)(5•X) (5•X2)2
= -25X2 / 25•X4 = - X-2
Chain Rule Y = G [ H(X) ]
dY/dX = (dG/dH)•(dH/dX) Y = (5 + 5•X)2
dY/dX = 2(5 + 5•X)1(5) = 50 + 50•X
Quick Differentiation Review
Applications of Calculus in Managerial Economics
maximization problem: A profit function might look like an arch, rising to a peak and then declining at even larger outputs. A firm might sell huge amounts at very low prices, but discover that profits are low or negative.
At the maximum, the slope of the profit function is zero. The first order condition for a maximum is that the derivative at that point is zero.
If = 50·Q - Q2, then d/dQ = 50 - 2·Q, using the rules of differentiation.
Hence, Q = 25 will maximize profits where 50 - 2•Q = 0.
More Applications of Calculus minimization problem: Cost minimization supposes that
there is a least cost point to produce. An average cost curve might have a U-shape. At the least cost point, the slope of the cost function is zero.
The first order condition for a minimum is that the derivative at that point is zero.
If C = 5·Q2 - 60·Q, then dC/dQ = 10·Q - 60. Hence, Q = 6 will minimize cost where 10•Q - 60 = 0.
More Examples Competitive Firm: Maximize Profits
where = TR - TC = P•Q - TC(Q) Use our first order condition:
d/dQ = P - dTC/dQ = 0. Decision Rule: P = MC.
TC a function of Q
Max = 100•Q - Q2
100 -2•Q = 0 implies Q = 50 and = 2,500
Max= 50 + 5•X2
So, 10•X = 0 implies Q = 0 and= 50
Problem 1 Problem 2
Second Derivatives and the Second Order Condition:One Variable If the second derivative is negative, then it’s
a maximum If the second derivative is positive, then it’s a
minimum
Max = 100•Q - Q2
100 -2•Q = 0
second derivative is: -2 implies Q =50 is a MAX
Max= 50 + 5•X2
10•X = 0
second derivative is: 10 implies Q = 0 is a MIN
Problem 1 Problem 2
Partial Differentiation
Economic relationships usually involve several independent variables.
A partial derivative is like a controlled experiment -- it holds the “other” variables constant
Suppose price is increased, holding the disposable income of the economy constant as in Q = f (P, I ), then Q/P holds income constant.
Example Sales are a function of advertising in
newspapers and magazines ( X, Y) Max S = 200X + 100Y -10X2 -20Y2 +20XY Differentiate with respect to X and Y and set
equal to zero.
S/X = 200 - 20X + 20Y= 0
S/Y = 100 - 40Y + 20X = 0 solve for X & Y and Sales
Solution: 2 equations & 2 unknowns
200 - 20X + 20Y= 0 100 - 40Y + 20X = 0 Adding them, the -20X and +20X cancel, so
we get 300 - 20Y = 0, or Y =15 Plug into one of them:
200 - 20X + 300 = 0, hence X = 25 To find Sales, plug into equation: S =
200X + 100Y -10X2 -20Y2 +20XY = 3,250
Most decisions involve a gamble Probabilities can be known or unknown, and
outcomes possibilities can be known or unknown Risk -- exists when:
Possible outcomes and probabilities are known
Examples: Roulette Wheel or Dice We generally know the probabilities We generally know the payouts Uncertainty if probabilities and/or payouts are unknown
Concepts of Risk
When probabilities are known, we can analyze risk using probability distributions Assign a probability to each state of nature, and be
exhaustive, so thatpi = 1 States of NatureStrategy Recession Economic Boom
p = .30 p = .70
Expand Plant - 40 100Don’t Expand - 10 50
Payoff Matrix
Payoff Matrix shows payoffs for each state of nature, for each strategy
Expected Value = r= ri pi
r = ri pi = (-40)(.30) + (100)(.70) = 58 if Expand
r = ri pi = (-10)(.30) + (50)(.70) = 32 if Don’t Expand
Standard Deviation = = (ri - r ) 2. pi
_
_
-
Example of Finding Standard Deviations
expand = SQRT{ (-40 - 58)2(.3) + (100-58)2(.7)}
= SQRT{(-98)2(.3)+(42)2 (.7)}
= SQRT{ 4116} = 64.16
don’t = SQRT{(-10 - 32)2 (.3)+(50 - 32)2 (.7)}
= SQRT{(-42)2 (.3)+(18)2 (.7) }
= SQRT{ 756 } = 27.50
Expanding has a greater standard deviation (64.16), but also has the higher expected return (58).
FIGURE 2.9 A Sample Illustration of Areas under the Normal Probability Distribution Curve
Coefficients of Variationor Relative Risk Coefficient of Variation (C.V.) = / r.
C.V. is a measure of risk per dollar of expected return. Project T has a large standard deviation of $20,000
and expected value of $100,000. Project S has a smaller standard deviation of $2,000
and an expected value of $4,000. CVT = 20,000/100,000 = .2
CVS = 2,000/4,000 = .5 Project T is relatively less risky.
_
Projects of Different Sizes: If double the size, the C.V. is not changed!!!
Coefficient of Variation is good for comparing projects of different sizes
Example of Two Gambles
A: Prob X } R = 15.5 10 } = SQRT{(10-15)2(.5)+(20-15)2(.5)].5 20 } = SQRT{25} = 5
C.V. = 5 / 15 = .333B: Prob X } R = 30
.5 20 } = SQRT{(20-30)2 ((.5)+(40-30)2(.5)]
.5 40 } = SQRT{100} = 10C.V. = 10 / 30 = .333
A: Prob X } R = 15.5 10 } = SQRT{(10-15)2(.5)+(20-15)2(.5)].5 20 } = SQRT{25} = 5
C.V. = 5 / 15 = .333B: Prob X } R = 30
.5 20 } = SQRT{(20-30)2 ((.5)+(40-30)2(.5)]
.5 40 } = SQRT{100} = 10C.V. = 10 / 30 = .333
What Went Wrong at LTCM? Long Term Capital Management was a ‘hedge
fund’ run by some top-notch finance experts (1993-1998)
LTCM looked for small pricing deviations between interest rates and derivatives, such as bond futures.
They earned 45% returns -- but that may be due to high risks in their type of arbitrage activity.
The Russian default in 1998 changed the risk level of government debt, and LTCM lost $2 billion
Table 2.10 Realized Rates of Returns and Risk
Which had the highest return? Why?