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 P0P0 Q0Q0 P1P1 Q1Q1 An increase in price causes a decrease in quantity demanded.

Change in Quantity Demanded Quantity Price P0P0 Q0Q0 P1P1 Q1Q1 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 Sam +Diane = Market Q = f( P, P s, P c, Y, N P E ) ? + + P is price of the good P S is the price of substitute goods P C is the price of complementary goods Y is income, N is population, P E is the expected future price

Determinants of the Quantity Demanded i. price, P ii. price of substitute goods, P s iii. price of complementary goods, P c iv. income, Y v. advertising, A vi. advertising by competitors, A c vii. size of population, N, viii. expected future prices, P e xi. adjustment time period, T a 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 P0P0 Q0Q0 Q1Q1 An increase in demand refers to a rightward shift in the market demand curve.

Change in Demand Quantity Price P0P0 Q1Q1 Q0Q0 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 P1P1 Q1Q1 P0P0 Q0Q0 A decrease in price causes a decrease in quantity supplied.

Change in Quantity Supplied Quantity Price P0P0 Q0Q0 P1P1 Q1Q1 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 Acme Inc. + Universal Ltd. = Market Q = g( P, P I, RC, T, T/S) ?

i.price, P ii.input prices, P I, e.g., sheet metal iii.Price of unused substitute inputs, P UI, 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, T A 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 P0P0 Q1Q1 Q0Q0 An increase in supply refers to a rightward shift in the market supply curve.

Change in Supply Quantity Price P0P0 Q1Q1 Q0Q0 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 supplie d.

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, P e D S PePe Q P Willing & Able in cross- hatched

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? D S e1e1 P Q P1P1

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 D S e1e1 P Q D’ e2e2

Market Equilibrium Quantity Price P0P0 Q0Q0 D0D0 S0S0 Q1Q1 P1P1 D1D1 An increase in demand will cause the market equilibrium price and quantity to increase.

Market Equilibrium Quantity Price P1P1 Q1Q1 S0S0 Q0Q0 P0P0 D0D0 D1D1 A decrease in demand will cause the market equilibrium price and quantity to decrease.

Market Equilibrium Quantity Price P0P0 Q0Q0 D0D0 S0S0 Q1Q1 P1P1 An increase in supply will cause the market equilibrium price to decrease and quantity to increase. S1S1

Market Equilibrium Quantity Price P1P1 Q1Q1 D0D0 Q0Q0 P0P0 A decrease in supply will cause the market equilibrium price to increase and quantity to decrease. S1S1 S0S0

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 GLOBAL MAX 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 PVIF n =[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 NCF t / ( 1 + r t ) t where NCF t 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 2A Differential 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 M y =  Y/  X For a very small change in X, the derivative is written: dY/dX = limit  Y/  X  X  B

Marginal = Slope = Derivative The slope of line C-D is  Y/  X The marginal at point C is M y 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 D Y YY X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 = cXdY/dX = cY = 5X dY/dX = 5 Power Y = cX b dY/dX = bcX b-1 Y = 5X 2 Functions dY/dX = 10X Name Function Derivative Example

Sum of Y = G(X) + H(X) dY/dX = dG/dX + dH/dX Functions exampleY = 5X + 5X 2 dY/dX = X Product of Y = G(X)H(X) Two Functions dY/dX = (dG/dX)H + (dH/dX)G example Y = (5X)(5X 2 ) dY/dX = 5(5X 2 ) + (10X)(5X) = 75X 2 Quick Differentiation Review

Quotient of Two Y = G(X) / H(X) Functions dY/dX = (dG/dX)H - (dH/dX)G H 2 Y = (5X) / (5X 2 ) dY/dX = 5(5X 2 ) -(10X)(5X) (5X 2 ) 2 = -25X 2 / 25X 4 = - X -2 Chain RuleY = G [ H(X) ] dY/dX = (dG/dH)(dH/dX) Y = (5 + 5X) 2 dY/dX = 2(5 + 5X) 1 (5) = 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 - Q 2, then d  /dQ = ·Q, using the rules of differentiation. Hence, Q = 25 will maximize profits where 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·Q ·Q, then dC/dQ = 10·Q Hence, Q = 6 will minimize cost where 10Q - 60 = 0.

More Examples Competitive Firm: Maximize Profits where  = TR - TC = PQ - TC(Q) Use our first order condition: d  /dQ = P - dTC/dQ = 0. Decision Rule: P = MC. TC a function of Q l Max  = 100Q - Q Q = 0 implies Q = 50 and  = 2,500 l Max  = X 2 So, 10X = 0 implies Q = 0 and  = 50 Problem 1Problem 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 l Max  = 100Q - Q Q = 0 second derivative is: -2 implies Q =50 is a MAX l Max  = X 2 10X = 0 second derivative is: 10 implies Q = 0 is a MIN Problem 1Problem 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 -10X 2 -20Y 2 +20XY Differentiate with respect to X and Y and set equal to zero.  S/  X = X + 20Y= 0  S/  Y = Y + 20X = 0 solve for X & Y and Sales

Solution: 2 equations & 2 unknowns X + 20Y= Y + 20X = 0 Adding them, the -20X and +20X cancel, so we get Y = 0, or Y =15 Plug into one of them: X = 0, hence X = 25 To find Sales, plug into equation: S = 200X + 100Y -10X 2 -20Y 2 +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 that   p i = 1 States of Nature StrategyRecessionEconomic Boom p =.30 p =.70 Expand Plant Don’t Expand

Payoff Matrix Payoff Matrix shows payoffs for each state of nature, for each strategy Expected Value = r  =  r i  p i r =  r i p i = (-40)(.30) + (100)(.70) = 58 if Expand r =  r i p i = (-10)(.30) + (50)(.70) = 32 if Don’t Expand Standard Deviation =  =    (r i - r ) 2. p i _ _ -

Example of Finding Standard Deviations  expand = SQRT{ ( ) 2 (.3) + (100-58) 2 (.7)} = SQRT{(-98) 2 (.3)+(42) 2 (.7)} = SQRT{ 4116} =  don’t = SQRT{( ) 2 (.3)+( ) 2 (.7)} = SQRT{(-42) 2 (.3)+(18) 2 (.7) } = SQRT{ 756 } = 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 Variation or 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. CV T = 20,000/100,000 =.2 CV S = 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 = }  = SQRT{(10-15) 2 (.5)+(20-15) 2 (.5)].520} = SQRT{25} = 5 C.V. = 5 / 15 =.333 B: Prob X }R = }  = SQRT{(20-30) 2 ( (.5)+(40-30) 2 (.5)].540} = SQRT{100} = 10 C.V. = 10 / 30 =.333 A: Prob X }R = }  = SQRT{(10-15) 2 (.5)+(20-15) 2 (.5)].520} = SQRT{25} = 5 C.V. = 5 / 15 =.333 B: Prob X }R = }  = 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 Management was a ‘hedge fund’ run by some top-notch finance experts ( ) 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?