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# Fundamental Economic Concepts - PowerPoint PPT Presentation

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

Chapter 2

• 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

• 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.

Price

An increase in price causes a decrease in quantity demanded.

P1

P0

Quantity

Q1

Q0

Price

A decrease in price causes an increase in quantity demanded.

P0

P1

Quantity

Q0

Q1

• 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

• 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.

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

Price

P0

Quantity

Q0

Q1

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

Price

P0

Quantity

Q1

Q0

• 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.

A decrease in price causes a decrease in quantity supplied.

Price

P0

P1

Quantity

Q1

Q0

An increase in price causes an increase in quantity supplied.

Price

P1

P0

Quantity

Q0

Q1

• 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

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

x. taxes or subsidies, T/S

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

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

Price

P0

Quantity

Q0

Q1

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

Price

P0

Quantity

Q1

Q0

• 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

• 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.

• 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 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

• 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 for the 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!

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

exampleY = (5•X)(5•X2 )

dY/dX = 5(5•X2 ) + (10•X)(5•X) = 75•X2

• 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

• 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.

• 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.

• 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

• 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 1 Problem 2

• Max = 100•Q - Q2

• 100 -2•Q = 0

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

• 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.

• 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

• 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 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 Variation Probability Distribution Curveor 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: Probability Distribution CurveIf 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 = .333

B: Prob X } R = 30

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

.5 40 } = SQRT{100} = 10

C.V. = 10 / 30 = .333

What Went Wrong at LTCM? Probability Distribution Curve

• 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 Probability Distribution Curve

• Which had the highest return? Why?