Econ 154a Problem Set 2

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: I. Analytical Problem 1 1. Y = MPN = d/dN(AK N 1- ) = (1- )AK N- = 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 N 1- ) = (- )(1- )AK N-1- = -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- )AK N- = 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 + L = U(N) = w N + (N max N) = ( w )N + N max 5. dU(N)/dN = w . If w > , 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 < , then dU(N)/dN = w 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 = , then dU(N)/dN = w 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- )AK N- = 0.7*N-0.3 = w = = 0.8. = 0....
View Full Document

Page1 / 8

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online