Unformatted text preview: 2. Suppose the aggregate demand curve is given by 93(10) = a + bp + cp2 for p 6 [0,12], where
a. > 0, :r’(p) < 0. There are three ﬁrms with cost functions given by cj(q_,) : ”Iggy 2+1 for je {1,2,3}. (a) Solve for the aggregate supply function. What is the market clearing price and quantity?
What is it if a = 100,b = 73,3 = 74/9? What is it ifa = 100,11 = 63—1,c = 1? (b) Now the government levies a sales tax. Find the marginal effect of the tax on the price.
How does the tax burden shift between consumers and producers as a function of a, b,
and c? (c) What is the marginal effect of the tax on the price if a = 100, b = —3, c = —4/Q? What
is it ifa:100,b: 53—1,c: 1? 6. There are two consumers with utility functions u1(a:11,:c21) = 3;?13531 and u2($12,$22) = 55121822. There are two ﬁrms with technologies that transform good 1 into good 2: f1(211) :
102916 and f2(z12) : 202922. Consumer 1’s shares of the ﬁrms is 6'1 : (1/3, 1/2) and consumer
2’s shares of the ﬁrms is 62 : (2/3, 1/2). The consumer’s are endowed with an : (100, 0) and mg 2 (50, 10).
(a) Solve for the ﬁrst order conditions of the consumers and the ﬁrms. (b) Solve for the competitive equilibrium.
((1) What is the ﬁrm’s proﬁt? ...
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 Fall '16

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