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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

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Fundamental Economic Concepts

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## 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

Price

An increase in price causes a decrease in quantity demanded.

P1

P0

Quantity

Q1

Q0

### Change in Quantity Demanded

Price

A decrease in price causes an increase in quantity demanded.

P0

P1

Quantity

Q0

Q1

### 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

\$5

20

Q /time unit

Sam +Diane = Market

• The Market Demand Curve is the horizontal sum of the individual demand curves.

• The Demand Functionincludes all variables that influence the quantity demanded

4 3 7

Q = f( P, Ps, Pc,Y, N PE)

- + - ? + +

P is price of the good

PS is the price of substitute goods

PC is the price of complementary goods

Y is income, N is population,

PE is the expected future price

### Determinants of the Quantity Demanded

i. price, P

ii. price of substitute goods, Ps

iii. price of complementary goods, Pc

iv. income, Y

vii. size of population, N,

viii. expected future prices, Pe

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

An increase in demand refers to a rightward shift in the market demand curve.

Price

P0

Quantity

Q0

Q1

### Change in Demand

A decrease in demand refers to a leftward shift in the market demand curve.

Price

P0

Quantity

Q1

Q0

### 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

A decrease in price causes a decrease in quantity supplied.

Price

P0

P1

Quantity

Q1

Q0

### Change in Quantity Supplied

An increase in price causes an increase in quantity supplied.

Price

P1

P0

Quantity

Q0

Q1

### 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

Acme Inc. + Universal Ltd. = Market

• 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

Q = g( P, PI, RC,T, T/S)

+ - - + ?

Determinants of the Supply Function

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

x.taxes or subsidies, T/S

Note: Anything that shifts supply can be included and varies for different industries or products.

### Change in Supply

An increase in supply refers to a rightward shift in the market supply curve.

Price

P0

Quantity

Q0

Q1

### Change in Supply

A decrease in supply refers to a leftward shift in the market supply curve.

Price

P0

Quantity

Q1

Q0

### 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

S

• Superimpose demand and supply

• If No Excess Demand and No Excess Supply . . .

• Then no tendency to change at the equilibrium price, Pe

P

Willing

& Able

in cross-

hatched

Pe

D

Q

### Dynamics 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?

P

S

P1

e1

D

Q

### 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 well

P

S

e2

D’

e1

D

Q

D1

P1

Q1

### Market Equilibrium

Price

D0

S0

An increase in demand will cause the market equilibrium price and quantity to increase.

P0

Quantity

Q0

D1

P0

P1

Q1

Q0

### Market Equilibrium

Price

D0

S0

A decrease in demand will cause the market equilibrium price and quantity to decrease.

Quantity

S0

S1

P1

Q1

### Market Equilibrium

Price

An increase in supply will cause the market equilibrium price to decrease and quantity to increase.

D0

P0

Quantity

Q0

S1

S0

P1

P0

Q1

Q0

### Market Equilibrium

Price

A decrease in supply will cause the market equilibrium price to increase and quantity to decrease.

D0

Quantity

### 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

profit

GLOBAL

MAX

MAX

A

quantity B

### Average Profit = Profit / Q

• Slope of ray from the origin

• Rise / Run

• Profit / Q = average profit

• Maximizing average profit doesn’t maximize total profit

PROFITS

MAX

C

B

profits

quantity

Q

### 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.

### 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:

• high expected future net cash flows

• low initial outlays

• low rates of discount

### Sources of Positive NPVs

• Brand preferences for established brands

• Ownership control over distribution

• Patent control over products or techniques

• Exclusive ownership over natural resources

• Inability of new firms to acquire factors of production

• Economies of large scale or size from either:

• Capital intensive processes, or

• 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 = DY/DX

• For a very small change in X, the derivative is written:

dY/dX = limit DY/DX

DX  B

### Marginal = Slope = Derivative

• The slope of line C-D is DY/DX

• The marginal at point C is My is DY/DX

• The slope at point C is the rise (DY) over the run (DX)

• The derivative at point C is also this slope

D

Y

DY

DX

C

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 = cdY/dX = 0Y = 5

FunctionsdY/dX = 0

• A Line Y = c•XdY/dX = cY = 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

### Quick Differentiation Review

• Sum of Y = G(X) + H(X) dY/dX = dG/dX + dH/dX

Functions

exampleY = 5•X + 5•X2dY/dX = 5 + 10•X

• Product of Y = G(X)•H(X)

Two FunctionsdY/dX = (dG/dX)H + (dH/dX)G

exampleY = (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 RuleY = 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

### 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

Problem 1Problem 2

• 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

### 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= 50 + 5•X2

• 10•X = 0

• second derivative is: 10 implies Q = 0 is a MIN

Problem 1Problem 2

• Max = 100•Q - Q2

• 100 -2•Q = 0

• second derivative is: -2 implies Q =50 is a MAX

### 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

Risk

• 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 thatpi = 1

States of Nature

StrategyRecessionEconomic Boom

p = .30p = .70

Expand Plant- 40 100

Don’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).

### Coefficients of Variationor Relative Risk

_

• Coefficient of Variation (C.V.) = / r.

• C.V. is a measure of risk per dollar of expected return.

• Project Thas 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

.510} = SQRT{(10-15)2(.5)+(20-15)2(.5)]

.520} = SQRT{25} = 5

C.V. = 5 / 15 = .333

B: Prob X }R = 30

.520}  = SQRT{(20-30)2 ((.5)+(40-30)2(.5)]

.540} = SQRT{100} = 10

C.V. = 10 / 30 = .333

### What Went Wrong at LTCM?

• Long Term Capital Managementwas 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?