Econ 154a Problem Set 2

# Econ 154a Problem Set 2 - I Analytical Problem 1 1 Y’ =...

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Unformatted text preview: I. Analytical Problem 1 1. Y’ = MPN = d/dN(AK α N 1- α ) = (1- α )AK α N- α = 0.7. Since the MPN is always positive, the production function for this firm indicates that the firm does not experience diminishing product of labor. However, because Y’’ = MPN’ = d 2 /dN 2 (AK α N 1- α ) = (- α )(1- α )AK α N-1- α = -0.21, the firm does experience a diminishing marginal product of labor (id est, each additional unit of labor increases production [so the production function does not have decreasing returns to labor], but each unit of labor adds less to the overall productivity [the production function exhibits diminishing marginal labor returns]). 2. MPN = (1- α )AK α N- α = 0.7*N-0.3 = w . The profit a firm reaps from hiring a new worker is given by P = MPN – w . A profit maximizing firm will therefore hire any worker such that P = MPN – w ≥ 0(the firm will hire all workers such that it will reap a profit from each worker). Rearranging, the firm will hire such that MPN ≥ w . This is a closed set of workers with a boundary at MPN = w . Thus, it is intuitive that a firm should ascertain this boundary point in order to determine how many workers it should hire. 3. Graph of labor demand with employment N on the horizontal axis and real wage w on the vertical axis. Labor Demand 0.2 0.4 0.6 0.8 1 1.2 10 20 30 40 50 60 70 80 90 100 N w ND 4. U (C,L) = C + λ L = U(N) = w N + λ (N max – N) = ( w – λ )N + λ N max 5. dU(N)/dN = w – λ . If w > λ , then dU(N)/dN is positive for all values of N and the utility function will increase as N increases for all values of N. Therefore, the worker will supply as much labor as possible in order to maximize utility – id est N max units of labor. 6. If w < λ , then dU(N)/dN = w – λ is negative for all values of N and the utility function will decrease as N increases for all values of N. Therefore, the worker will supply as little labor as possible in order to maximize utility – id est 0 units of labor. 7. If w = λ , then dU(N)/dN = w – λ is zero for all values of N and the utility function will be completely independent of the value of N. Therefore, the worker will be indifferent about how much she works. 8. Labor Market Graph: Labor Market 0.5 1 1.5 2 2.5 3 0.2 0.4 0.6 0.8 1 1.2 N w ND NS 9. Equilibrium Employment, Wage and Output i. MPN = (1- α )AK α N- α = 0.7*N-0.3 = w = λ = 0.8. = 0....
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## This note was uploaded on 07/19/2008 for the course ECON 154 taught by Professor Bjoernbruegemann during the Fall '07 term at Yale.

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Econ 154a Problem Set 2 - I Analytical Problem 1 1 Y’ =...

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