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ECMA04H - VERSION A Sketchy Solutions to First Term Test, written on October 20, 2006 These are the answers to VERSION A. Q1: C On the PPF, if X = 7, Y = 20 - 12.8 = 7.2, so the point (7,7.4) is unattainable Q2: E opportunity cost of X = -dY/dX = .4(1+X); at X = 3, cost = 1.6 Q3: B opportunity cost of Y = -dX/dY at X = 5, -dY/dX = 2.4, so -dX/dY = 5/12 Q4: E V = 2X + 20 - .2(1+X)2 to maximize, set dV/dX = 0 dV/dX = 2 - .4(1+X) = 0 so .4(1+X) = 2, 1+X = 5, X = 4 Q5: F I is false because the PPF has nothing to do with tastes; II is true because bowing out means that the opportunity cost of X rises as X increases; III is true because the PPF is the boundary between attainable and unattainable, indicating that there are limited amounts of X and Y, hence scarcity. Q6: A The rise in income shifts demand to the right Q7: H If wages rise in the tennis racquet industry, supply shifts to the left. Meanwhile, if golf clubs fall in price, this reduces the demand for tennis racquets, because golf clubs and tennis racquets are substitutes. D shifts left. Quantity clearly falls, but we are not sure what happens to price, because the effects on P* go in opposite directions. Q8: G If tennis court rentals fall in price, this increases the demand for tennis racquets, because tennis courts and tennis racquets are complements. D shifts right. Meanwhile, the technological innovation shifts supply to the right. Quantity clearly rises, but we are not sure what happens to price, because the effects on P* go in opposite directions. Q9: I The newspaper story increases the demand for tennis racquets, so D shifts to the right; the fall in the price of the substitute (golf clubs) reduces the demand, so D shifts to the left. So we don’t know which way the demand curve shifts overall: if left, P* and Q* fall; if right, P* and Q* rise; but if the two effects cancel out, then demand doesn’t shift at all and nothing changes. Q10: D If wages fall in the tennis racquet industry, supply shifts to the right. The technological innovation also shifts supply to the right. Therefore, P* falls and Q* rises. Q11: B Q12-15: The kink in the demand curve makes the computation a bit harder. Q12: E If P = 3, then X = 18; consumer surplus is between the demand curve and the $3 price line, but does not form a simple triangle and so you must divide the consumer surplus area to work it out. Q13: H If the consumer pays nothing for each additional unit, the consumer will set X=36. The total value of these units to the consumer is the area Q14: D Q15: G Q16: I Q17: E Q18: E Q19-20 Q19: A Q20: E Q21: A Q22: I Q23-25: Q23: H Q24: C Q25: B under the demand curve, which can be found to be $114. If the allinclusive payment is F, then consumer surplus will be 114-F, and the consumer will choose this option if 114-F>33. In other words, F cannot be greater than $81. If P = 6, then X = 4, and tax revenue = unit tax times X = $3 x 4 = $12 The deadweight area is no longer a simple triangle, but it can be computed by dividing up the area. The correct answer is $17. The demand curve can be obtained by setting P = dU/dX = 36(X+1)-.5 P = 4 = 36(X+1)-.5 so (X+1).5 = 9 so X+1 = 81 so X = 80. U(80) = 72(81).5 - 72 = 576 and U(0) = 0 and PX = $320 So CS = 576 - 320 = $256. You can do this by formulas, or intuitively by looking at graphs. I and III are true statements. dP/dQ = -b, so elasticity of demand = -(dQ/dP)(P/Q) = (1/b)(100/120) = 5/(6b). b = 2/3, so elasticity = 5/(6b) = 5/4 elasticity = 1 = 5/(6b), so b = 5/6 This is a hard question. TR = PQ So dTR/dP = Q + PdQ/dP = Q[1 + (P/Q)dQ/dP] = Q[1 - elasticity] If elasticity = 2/5 and Q = 600, then dTR/dP = 600[3/5] = 360 If P changes by .25, then TR changes by 360 x .25 = 90 BS/SS = elasticity of supply/elasticity of demand = 1.2/.3 = 4; thus BS/SS = .8/.2 or BS = 8/10 or BS = .8 PB = 100 - Q and PS = 20 + (1/3)Q and PB = PS + 12 Thus 100 - Q = 32 + (1/3)Q or (4/3)Q = 68 or Q = 51 Q = 51 so PB = 100 - 51 = $49 Q = 51 so PS = 20 + (1/3)(51) = $37 As we have shown, changes in the law do not affect the buyers’ share and the sellers’ share.