720 • ANSWERS TO SELECTED EXERCISES CHAPTER a For computer chips, EP = - 2, so - = %⌬Q/10, and therefore %⌬Q = - 20 For disk drives, EP = - 1, so a 10 percent increase in price will reduce sales by 10 percent Sales revenue will decrease for computer chips because demand is elastic and price has increased To estimate the change in revenue, let TR1 = P1Q1 be revenue before the price change and TR2 = P2Q2 be revenue after the price change Therefore ⌬TR = P2Q2 - P1Q1, and thus ⌬TR = (1.1P1)(0.8Q1) - P1Q1 = - 0.12P1Q1 , or a 12 percent decline Sales revenue for disk drives will remain unchanged because demand elasticity is -1 b Although we know the responsiveness of demand to change in price, we need to know the quantities and the prices of the products to determine total sales revenues 11 a With small changes in price, the point elasticity formula would be appropriate But here, the price of food increases from $2 to $2.50, so arc elasticity should be used: Ep = (⌬Q/⌬P)(P/Q) We know that Ep = - 1, P = 2, ⌬P = 50, and Q = 5000 So, if there is no change in income, we can solve for ⌬Q: - = (⌬Q/.50) [((2 + 50)/2)/(5000 + ⌬Q/2)] = (⌬Q # 2.50)/(10,000 + ⌬Q) We find that ⌬Q = - 1000: she decreases her consumption of food from 5000 to 4000 units b A tax rebate of $2500 implies an income increase of $2500 To calculate the response of demand to the tax rebate, we use the definition of the arc income elasticity: EI = (⌬Q/⌬I)(I/Q) We know that EI = 0.5, I = 25,000, ⌬I = 2500, and Q = 4000 We solve for ⌬Q:0.5 = (⌬Q/2500)[((25,000 + 27,500)/2)/(4000 + (⌬Q/2)] Since ⌬Q = 195, she increases her consumption of food from 4000 to 4195 units However, she did not choose to return to her original bundle We can therefore infer that she found a better bundle that gave her a higher level of utility 13 a The demand curve is a straight line with a vertical intercept of P = 15 and a horizontal intercept of Q = 30 b If there were no toll, the price P would be 0, so that Q = 30 c If the toll is $5, Q = 20 The consumer surplus lost is the difference between consumer surplus when P = and consumer surplus when P = 5, or $125 CHAPTER 4—APPENDIX The first utility function can be represented as a series of straight lines; the second as a series of hyperbolas in the positive quadrant; and the third as a series of “L”s Only the second utility function meets the definition of a strictly convex shape The Slutsky equation is dX/dPX = 0X/0P*|U = U* - X(⌬X/⌬I), where the first term represents the substitution effect and the second term represents the income effect With this type of utility function the consumer does not substitute one good for the other when the price changes, so the substitution effect is zero CHAPTER The four mutually exclusive states are given in Table below The expected value is EV = (0.4)(100) + (0.3)(30) + (0.3)( -30) = $40 The variance is s = (0.4)(100 - 40)2 + (0.3)(30 - 40)2 + (0.3)(- 30 - 40)2 = 2,940 Initially, total wealth is $450,000 We calculate expected wealth under three options Under the safe option, E(U) = (450,000 + 1.05*200,000).5 = 678 With the summer corn crop, E(U) = 7(250,000 + 500,000).5 + 3(250,000 + 50,000).5 = 770 Finally, with the drought resistant summer corn crop, E(U) = 7(250,000 + 450,000).5 + 3(250,000 + 350,000).5 = 818 The option with the highest expected utility is planting the drought resistant crop c Felicia is better off after the rebate The amount of the rebate is enough to allow her to purchase her original bundle of food and other goods Recall that originally she consumed 5000 units of food When the price went up by fifty cents per unit, she needed an extra (5000)($0.50) = $2500 to afford the same quantity of food without reducing the quantity of the other goods consumed This is the exact amount of the rebate TABLE Slow growth rate Fast growth rate CONGRESS PASSES TARIFF CONGRESS DOES NOT PASS TARIFF State 1: State 2: Slow growth with tariff Slow growth without tariff State 3: State 4: Fast growth with tariff Fast growth without tariff