(Long-run costs,) Carmela's pasta factory employs workers and pasta machines according to the lowing production function f(L,K) = 10.5K0.5 e hourly cost of capital is $10 and the hourly cost of workers is $40. Write out the Lagrangian for the cost-minimization problem. Using the first order conditions of the Lagrangian, derive the optimal capital to labor ratio. Describe long-run output expansion path. Suppose Carmela wishes to produce 1000 units of pasta. How much labor and capital should she ploy? How much will it cost to produce? An order arrives doubling the amount of pasta Carmela needs to produce. Assuming she is unable t rchase more capital, how much will it cost to meet the new production level? In the long run Carmola will be able to ampl mora capital as well as labor. If Cormola continues

(Long-run costs,) Carmela's pasta factory employs workers and pasta machines according to the lowing production function f(L,K) = 10.5K0.5 e hourly cost of capital is $10 and the hourly cost of workers is $40. Write out the Lagrangian for the cost-minimization problem. Using the first order conditions of the Lagrangian, derive the optimal capital to labor ratio. Describe long-run output expansion path. Suppose Carmela wishes to produce 1000 units of pasta. How much labor and capital should she ploy? How much will it cost to produce? An order arrives doubling the amount of pasta Carmela needs to produce. Assuming she is unable t rchase more capital, how much will it cost to meet the new production level? In the long run Carmola will be able to ampl mora capital as well as labor. If Cormola continues

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A firm has the production function F(L, K) = L^1/2 + K^1/2The price of labor is $10 and the price of capital is $15. The firm has a production goal of Q = 100 units ofoutput.a) Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.
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6.