Midterm 2008

Midterm 2008 - x ? Suppose that initially P x = P y = 10...

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ECO 310 { Spring 2008 Microeconomic Theory { A Mathematical Approach Stephen Morris Midterm Examination Important instructions: 1. This is a closed-book examination. Put away your books, handouts, notes, calculators, palmtops, cellular phones, ::: now . 2. Print your name and your preceptor’s name clearly on the front cover of each answer booklet. Write your answers clearly. We won’t grade unreadable answers. 3. Answer each question in a separate booklet . 4. Write and sign the honor pledge { \I pledge my honor that I have not violated the honor code during this examination." { on the front cover of your answer booklet. 5. The examination is for 75 minutes. It will end promptly (among other reasons, because there is another exam immediately afterwards). Question 1: 45 minutes A consumer has expenditure function M ( P x ;P y ;u ) = P x e u , if u ln P y ± ln P x P y (ln P x ± ln P y + 1 + u ) , if u ² ln P y ± ln P x (i) What is the Hicksian (compensated) demand for good x ? (ii) What is the indirect utility function? (iii) What is the consumer’s Marshallian (uncompensated) demand for good
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Unformatted text preview: x ? Suppose that initially P x = P y = 10 and M = 10 and the price of good x is increased to P x = 20 (iv) How does the consumers demand for good x change if his income is held constant? (v) How does the consumers demand for good x change if his utility is held constant at the same level? (vi) What are the income and substitution e&ects of the price change from P x = 10 to P x = 20? 1 Question 2: 30 minutes Consider the production function Q = [ aK & + bL & ] 1 =& where Q is output, K is capital, L is labor, and a > 0, b > 0 and 0 < & < 1 are positive constants. Let p denote the price of output, and r , w the prices of the services of capital and labor respectively. When a &rm minimizes its cost, let R = r K= ( pQ ) ; W = w L= ( pQ ) be the shares of capital and labor costs in total cost. Find the cost minimizing conditional demand for inputs of the &rm and show that, as w=r increases, W=R falls. 2...
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Midterm 2008 - x ? Suppose that initially P x = P y = 10...

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