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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

Fundamental Economic Concepts

Chapter 2


Fundamental economic concepts1

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

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

Change in Quantity Demanded

Price

An increase in price causes a decrease in quantity demanded.

P1

P0

Quantity

Q1

Q0


Change in quantity demanded1

Change in Quantity Demanded

Price

A decrease in price causes an increase in quantity demanded.

P0

P1

Quantity

Q0

Q1


Demand curves

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


Fundamental economic concepts

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

Determinants 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

Change in Demand

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

Price

P0

Quantity

Q0

Q1


Change in demand1

Change in Demand

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

Price

P0

Quantity

Q1

Q0


Figure 2 3 shifts in demand

Figure 2.3 Shifts in Demand


Law of supply

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

Change in Quantity Supplied

A decrease in price causes a decrease in quantity supplied.

Price

P0

P1

Quantity

Q1

Q0


Change in quantity supplied1

Change in Quantity Supplied

An increase in price causes an increase in quantity supplied.

Price

P1

P0

Quantity

Q0

Q1


Supply curves

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


Fundamental economic concepts

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)

+ - - + ?


Fundamental economic concepts

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

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.


Change in supply

Change in Supply

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

Price

P0

Quantity

Q0

Q1


Change in supply1

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

  • 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

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

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

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

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


Market equilibrium1

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


Market equilibrium2

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


Market equilibrium3

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


Market equilibrium4

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

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

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

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

FIGURE 2.8 Total, Average, and Marginal Profit Functions


Present value

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

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

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

  • Superior access to financial resources

  • Economies of large scale or size from either:

    • Capital intensive processes, or

    • High start up costs


Appendix 2a differential calculus techniques in management

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

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


Fundamental economic concepts

__ _______ ___ __ ___ __ ___ ______

  • 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

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 review1

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 review2

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

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

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

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

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

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.


Fundamental economic concepts

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

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


Fundamental economic concepts

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

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

  • 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

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

FIGURE 2.9 A Sample Illustration of Areas under the Normal Probability Distribution Curve


Coefficients of variation or relative risk

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

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

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

Table 2.10 Realized Rates of Returns and Risk

  • Which had the highest return? Why?


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