Suppose a consumer has quasi-linear utility: u(x1,x2 ) = 3x1^2/3 + x2 . The marginal utilities
are MU1(x) = 2x1^−1/3 and MU2 (x) = 1. Throughout this problem, assume p2 = 1
1.(a) Sketch an indifference curve for these preferences (label axes and intercepts).
(b) Compute the marginal rate of substitution.
(c) Assume w ≥ 8/p1^2 . Find the optimal bundle (this will be a function of p1 and w). Why do
we need the assumption w ≥ 8/p1^2 ?
(d) Sketch the demand function for good 1 (holding w and p2
constant).
(e) Suppose p1 = 2. Compute the consumer’s surplus.
(f) Now suppose the government imposes a tax on good 1, so that the price of good 1 becomes 2 + t for some t > 0. Compute the consumer’s surplus (this will be a function of t).
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