Assume that all prices and quantities are equal or more than 0.

solve by substituting out the values to set x2 to a certain value of x1 and same thing for price 1 and 2. Remember: budget constraint= p1x1+p2x2=m

A person's preference over services (good 1) and physical goods (good 2) is represented by the following Cobb-Douglas utility function:

u(x,y)=x^(1/3)*y^(2/3)

Throughout this problem, assume that the price of good 2 is p2=2

(refer to the properties of Cobb-Douglas utility)

Calculate the persons marginal rate of substitution.

Is the persons preference monotonic? Is it strictly convex? Show how

Do the indifference curves of the person'spreference intersect the good~1 axis or the good~2 axis (or both or neither)?Show how you got to the answer

For the rest of this question, assume the following. A person has income m=18to spend. But the government where the person lives has imposed a tax on physical goods (good 2) that works as follows: Each consumer can spend up to 10 on physical goods tax-free, but any additional spending on physical goods is taxed at a tax rate of 50%. Services are not taxed. Since the price of physical goods is p2=1 this means it faces the following budget constraint:

{p1x1+x2?18ifx2?10,

{p1x1+10+1.5(x2?10)?18ifx2>10,

Graph the budget constraint for this problem, making sure to put services on x axis and physical goods on y axis

It should be kinked

There are three corner candidates to consider as possible solutions to the choice problem, one at each intercept of the budget constraint and one at the kink. Which (if any) of these corner solutions can you eliminate before you even start to consider interior candidates? For each one, explain why or why not.

Solve the optimization problem. Explain how you found whether it is a corner solution or an interior solution

example below

If the consumer has income m and faces prices pi and p2, what is her optimal bundle? ANSWER: At the optimal bundle, MRS equals the price ratio: X2 P1 X2 2p1 2x1 Lx1 P2 P2 Substitute this into the budget constraint: pixi + 2pixi = m Solve for x1: x1 = x1(p1, p2, m) = m 3p1 Substitute back into the budget constraint and solve for x2: m X2 = X2(P1, p2, m) = 2m P1 3p1 + p2x2 = m # 3p2 What is the consumer's expenditure share for good 1, as a function of m, p1, and p2? ANSWER: The expenditure share is constant: pixi(P1, p2, m) = m