Suppose that a consumer’s utility function is U(x, y) = xy . The marginal utilities for...

Suppose that a consumer’s utility function is U(x, y) = xy . The marginal utilities for this utility function are MU_x= y and MU_y= x. The price of y is P_y = 1. The price of x is originally P_x = 9 and it then falls to P_x = 4. The consumer’s income is I = 72.
1. (15 points) What x-y combination (x_A*, y_A*) maximizes utility in the original situation where P_x = 9? Why?
2. (15 points) What x-y combination (x_C*, y_C*) maximizes utility in the new situation where P_x = 4? Why?
3. (15 points) The gross effect of the price change—the shift from (x_A*, y_A*) to (x_C*, y_C*)—can be broken down into two components: a substitution effect and an income effect. Find the portion of the shift that is due to the substitution effect alone.
4. (15 points) Then, find the portion of the shift that is due to the income effect alone.

[Note: each part of the question has a specific numerical answer.]

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Rahul Sunny answered 1 year ago

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