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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 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**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 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**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 • Superior access to financial resources • 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 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!**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**Quick Differentiation Review**• 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**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**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 1 Problem 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