Microeconomic problems

ECO 405: HW 3

Sean Fahle State University of New York at Buffalo

Spring 2016

Due date: Wednesday, March 30.

You are encouraged to collaborate with your classmates on this assignment. However, all students must individually write up and submit their own assignment. Assignments are due in class at the beginning of the lecture on the due date. Late assignments may receive no credit.

1. State whether the following are true or false and provide an explanation of your choice.

(a) If x is an inferior good, then a decrease in the price of y must cause consumption of y to increase.

(b) If an increase in the price of y causes consumption of x to decrease, then x must be an inferior good.

(c) If x is a normal good, then y must be price elastic.

2. For the utility function u(x, y) = x0.5 + y0.5, do the following:

(a) Derive Marshallian (uncompensated) demand functions x(px, py, I) and y(px, py, I). (Hint: Don’t just copy the Cobb-Douglas example from lecture.)

(b) Derive the Marshallian demand curve for x(px|py, I) when py = 10 and I = 100. (c) Derive equations for the Engel curves of x and y when px = 5 and py = 10.

3. Derive and graph Marshallian and Hicksian demand curves for the good x for a con- sumer with the following utility function:

u(x, y) = 2x + y

Assume that the price of y is py = 10 and income is I = 100.

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