PracticeQuestion_Ch12 econ 326.pdf

PracticeQuestion_Ch12 econ 326.pdf - Econ 326 Practice...

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Econ 326 Practice Question 6 (Chapter 12) Heejeong Kim 1. Suppose that when a firm produces and sells x units of a commodity, it has revenue R ( x ) = rx , where r is a positive parameter, while the cost is C ( x ) = x 2 . The profit is then π ( x, r ) = R ( x ) - C ( x ) = rx - x 2 . Find the optimal choice of x * to maximize the profit, and verify ∂π * ∂r > 0. 2. Consider the utility maximization problem U ( x, y ) = x + ay subject to the budget constraint px + qy = m where m > q 2 4 a 2 p . (a) Find the demand functions x * ( p, q, m, a ) and y * ( p, q, m, a ). (b) What is the maximized utility U * ( p, q, m, a ). (c) Find how the change in p affects ( x * , y * ). 3. Consider the utility maximization problem U ( x, y ) = xy subject to the budget constraint 3 x + y = 120. (a) Find the utility maximizing x old , y old and λ * . Check the second-order condition as well. (b) Now, price of x drops from 3 to 2.5. What is the new utility maximizing level of x new ? (c) From the change in x new - x old , find the substitution effect and income effect. 4. Suppose U ( x, y ) denotes the utility enjoyed by a person when having x hours of leisure per day (24 hours) and y units per day of other goods. The person gets an hourly wage of w
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