ps 1 solutions

ps 1 solutions - Intermediate Microeconomics Summer 2007...

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1 Intermediate Microeconomics Monika Thomas Summer 2007 Solutions: Problem Set 1 1.2 a) Surprisingly high export sales mean that the demand for corn was higher than expected, at D 2 rather than D 1 . b) Dry weather would reduce the supply of corn, to S 2 rather than S 1 . P Q S D 1 D 2 P 1 P 2 S 1 S 2 P Q D P 1 P 2

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2 c) Assuming the U.S. does not import corn, reduced production outside the U.S. would not impact U.S. corn market supply. El Nino would, however, cause demand for U.S. corn to shift out, the figure being the same as in part (a) above. 2.3 a) P Q 300 300 50 500 600 D S b) P P P P = = + = 50 6 300 4 300 2 600 Plugging 50 = P back into either the supply or demand equation yields 500 = Q . 2.9 a) Q P Q P P Q 7 1 50 350 7 7 350 = = = b) The choke price occurs at the point where 0 = Q . Setting 0 = Q in the inverse demand equation above yields 50 = P . c) At 50 = P , the choke price, the elasticity will approach negative infinity.
3 2.13 a) Substituting the values of R and T , we get P Q Supply P Q Demand s d 5 14 : 2 70 : + = = In equilibrium, 70 – 2 P = –14 + 5 P , which implies that P = 12. Substituting this value back, Q = 46. b) Elasticity of Demand = –2(12/46), or –0.52. Elasticity of Supply = 5(12/46) = 1.30. c) 43 . 0 ) 46 10 ( 2 tan , = = ium ti golf ε . The negative sign indicates that titanium and golf balls are complements, i.e., when the price of titanium goes up the demand for golf balls decreases. 2.15 a) 10000 100(300) 99(300) 9700 d U d U Q Q =− + = Using 300 U P = and 9700 d U Q = gives , 300 100 3.09 9700 QP ⎛⎞ ⎜⎟ ⎝⎠ b) Market demand is given by ddd UA QQQ =+ . Assuming the airlines charge the same price we have 10000 100 99 10000 100 99 20000 100 99 100 99 20000 2 d A U d d P P P P P P =−+ +−+ + + When 300 = P , 19400 d Q = . This implies an elasticity equal to , 300 2 .0309 19400

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4 Chapter 3 Consider two goods, A and B . For each of the following scenarios, develop the utility function ( , ) UAB that matches the given information. d) The consumer believes that goods A and B are perfect substitutes with one unit of A equivalent to three units of B . (,) 3 A B = + Page Reference: 87 e) The consumer believes that goods A and B are perfect complements and always uses three units of B for every unit of A . (,) m i n ( 3,) AB = Page Reference: 88-89
5 3.1 The two graphs are shown below. It can be seen from both graphs that this function does not satisfy the law of diminishing marginal utility. The first figure shows that utility increases with x , and moreover, that it increases at an increasing rate. For example, an increase in

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ps 1 solutions - Intermediate Microeconomics Summer 2007...

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