This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Practice Problem Set 2 ECON 11 Summer Session C 2010 Microeconomic Theory Yong Yang (You may not use calculators in the exam. The exam questions will have simpler numbers.) 1. Suppose Lynn has a utility function U = X 2 Y . She wants to use her income $90 to purchase goods X and Y . X costs $2 and Y costs $3. Answer the following. (a) Draw a budget line. (b) If she consumes 15 units of X and 20 units of Y, is it optimal? Explain. (c) Verify whether your answer to (b) is correct by solving for the optimal consumption. (d) Suppose the price of X increases to 3. Solve for the new optimal consumption. (e) Use your answers to (c) and (d) to draw an approximate demand curve for X . 2. Consider a utility function U = XY 2 . Answer the following. (a) Find the marginal utilities of goods X and Y . (b) Is the marginal utility of X decreasing in X ? Is the one of Y decreasing in Y ? (c) Is the marginal rate of substitution decreasing in X ? (d) Is the following statement true or false? “The marginal rate of substitution is diminishing only when the marginal utilities are decreasing.” 3. Consider two consumers Ted and Emily. Ted has a utility function U = XY and Emily has one U = √ XY . Both consumers live in the same city and face the same price: P X = 3 and P Y = 5. Answer the following. (a) Suppose Ted’s income is I T = 300. Find his optimal consumption. (b) Suppose Emily happens to have the same income I E = 300. Find her optimal consumption. Is it the same with or different from Ted’s optimal consumption? (c) Consider another consumer Alex who has a utility function U = ln X + ln Y . Note that a first order derivative of ln X with respect to X is 1 X . If Alex has an income I A = 300, what would be the optimal consumption for Alex? (d) Compare the MRS of the above three consumers. Is the following statement true or false?...
View
Full Document
 Summer '08
 cunningham
 Utility, optimal consumption

Click to edit the document details