1. Assume a consumer has as preference relation represented by u(x1; x2) = x1a + x2...

1. Assume a consumer has as preference relation represented by u(x₁; x₂) = x₁^a + x₂ for a E (0,1); with x E C = R²₊: Answer the following:

a. Show the preference relation this consumer is convex and strictly monotonic.

b. Compute the MRS between good 1 and good 2, and explain why it coincides with the slope of an indifference curve.

c. Write down the consumer optimization problem, and construct the first order conditions for this problem.

d. Define the value function for this consumer (follow my notes in class). Is the value function an increasing function increasing in income m? If we make good one the numeraire (i.e., the budget constraint is x1 + px2 < or = to m where p is the relative prices of good 2). Is the value function increasing or decreasing in the relative price of good 2?

Expert Solution

Rahul Sunny answered 2 years ago

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