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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?...
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- Summer '08
- Utility, optimal consumption