101A_midterm2sp

101A_midterm2sp - Econ 101A Midterm 2 Th 10 April 2008. You...

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Econ 101A — Midterm 2 Th 10 April 2008. You have approximately 1 hour and 20 minutes to answer the questions in the midterm. I will collect the exams at 11.00 sharp. Show your work, and good luck! Problem 1. Manager with Expected Utility (25 points) . A manager decides how much e f ort e to put in managing a company. We assume e [0 , 1] . The e f ort determines the probability of success, and hence the manager’s pay. With probability e, a project succeeds and the manager gets paid W> 0 . With probability 1 e, the project fails and the manager is f red (and hence is paid 0). The manager has initial wealth w and utility over consumption U ( c ) , with U 0 ( c ) > 0 for all c. The manager consumes all the income, including the initial wealth, after she is paid the salary (possibly zero). The cost of e f ort is e 2 / 2 . 1. Write the expected utility maximization of the manager with respect to e .(5po in t s ) 2. Write the f rst order condition and derive the solution e .(5po in t s ) 3. What is the e f ect of an increase in salary W on the optimal e f ort e ? Interpret the intuition. (5 points) 4. What is the e f ect of an increase in the initial wealth w on the optimal e f ort e ? Interpret the intuition, relating to what you know about attitude toward risk. (10 points) Solution of Problem 1. 1. The manager maximizes max e eU ( w + W )+(1 e ) U ( w ) e 2 / 2 . 2. The f rst order condition is U ( w + W ) U ( w ) e =0 and hence e = U ( w + W ) U ( w ) . 3. The e f ect of W is ∂e ∂W = U 0 ( w + W ) > 0 . 4. The e f ect of w is ∂e ∂w = U 0 ( w + W ) U 0 ( w ) . Whether this term is positive or negative depends on whether the marginal utility function U 0 () is increasing or not, that is, whether U () is convex or not. If U
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Problem 2. Pro f t Maximization with Taxes (96 points) We consider the market for widgets, which is characterized by the aggregate (inverse) demand function p ( X )= a bX, where X is the total quantity of widgets demanded in the market. The cost function of each company is c ( y )= cy α ,w ith c> 0 .
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This note was uploaded on 09/05/2009 for the course ECON 101a taught by Professor Staff during the Spring '08 term at Berkeley.

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101A_midterm2sp - Econ 101A Midterm 2 Th 10 April 2008. You...

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