Final Exam
Date: June 2, 2010
Subject: Advanced Microeconomics I (ECO600E) Professor: Yosuke YASUDA
1. True or False (9 points)
Answer whether each of the following statements is true (T) or false (F). You do NOT need to explain the reason.
(a) Hicksian demand of some good is ALWAYS (weakly) decreasing in its own price.
(b) Homothetic functions MUST be homogenous of degree one.
(c) For ANY risk averse decision maker, the RELATIVE risk aversion is indepen- dent of her wealth level.
2. Duality (10 points)
Suppose the (minimum) expenditure function is given by e(p1; p2; u) = 2upp1p2. (a) What are the Hicksian demand functions? (b) What is the indirect utility function?
(c) What are the Marshallian demand functions? 3. Production (16 points)
Suppose the production function takes the following form, y =pminf x1; x2g
where ; > 0. Let w1; w2 > 0 be the prices for inputs x1 and x2 respectively. Then, answer the following questions.
(a) Sketch the isoquant for this technology.
Hint: Isoquant is the combination of inputs that achieves a certain given level of output. (corresponds to “indi¤erence curve” in consumer theory.)
(b) Does this production function display increasing return or decreasing return to scale? Explain why.
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(c) Derive the (minimum) cost function, c(w1; w2; y).
Hint: Cost function is the value function of the cost minimization problem. (d) Let p > 0 be the price for output y. Describe the pro…t maximization problem
and solve it.
Hint: Although you can take either one-step or two-step procedure, the latter is much simpler. (note that you have already derived the cost function in (c).) 4. Expected Utility (15 points)
The vNM utility function is given by u(x) =px.
(a) Is the decision maker risk-averse, risk-neutral, or risk-loving? Explain why. (b) Show that the absolute risk aversion is decreasing in x.
(c) Consider the following lottery (gamble): x becomes $100 or $400 with proba- bility 0:5 each. Calculate the certainty equivalence and risk premium of this lottery.
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