Question

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).

2. (b) Compute the marginal rate of substitution.

3. (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).

5. (e) Suppose p1 = 2. Compute the consumer’s surplus.

6. (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).

Answer 1

Hi there! Thank you for the question. As per our Honor Code, we will only answer 4 sub-parts. So, we will answer the first 4. Please re-submit the question and specify the other parts (up to 4) you would like to be answered.

___________________________________________________________________________________________________