Eco 300, Spring 2011, Homework 2 Professor Rui Zhao Due Thursday, 02/17 1. (20 points) Suppose a consumer has the utility function U(x, y) = 2xy. The marginal utilities are MU x = 2y, MU y = 2x. Suppose price of x is P x = 1, price of y is P y = 2, and the consumer’s income is $12. a. In a clearly labeled graph draw the budget line and several indifference curves. Indicate where the optimal choice is. (You don’t need to draw the curves precisely for the equations, just illustrate the idea of the tangency condition.) b. Using algebra (the tangency equation and the budget equation) to find the optimal choice. c. At the optimal choice that you found, what is the marginal rate of substitution between x and y, i.e. MRS x,y ? d. Suppose the consumer decides to buy 4 units good x and 4 units y. What is the marginal utility per dollar spent on x (MU x /P x )? What is the marginal utility per dollar spent on y (MU y /P y )? What does this tell you about how the consumer should substitute one good for the other? (Hint: Compare to Learning-by-doing exercise 4.2)
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