A firm maximizes its profit functionpL0.5 – wL subject to wL = Kwhere L0,5 is its production function, L is aninput (labor), p is the market price, w is the unitcost of the labor L and K is a parameter.Profits are maximized for LKA with thewLagrange multiplier A =12wL-Using the envelope theorem evaluate the marginaleffect of a change of w on the maximal profitsassuming:p= 10, w = 1 and K = 100Answer:

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A firm maximizes its profit function pL0.5 – wL subject to wL = K where LO,5 is its production function, L is an input (labor), p is the market price, w is the unit cost of the labor L and K is a parameter. Profits are maximized for L = 4 with the Lagrange multiplier A - 1 2w I Using the envelope theorem evaluate the marginal effect of a change of w on the maximal profits assuming: p = 10, w = 1 and K = 100 Answer:

A firm maximizes its profit function pL0.5 – wL subject to wL = K where LO,5 is its production function, L is an input (labor), p is the market price, w is the unit cost of the labor L and K is a parameter. Profits are maximized for L = 4 with the Lagrange multiplier A - 1 2w I Using the envelope theorem evaluate the marginal effect of a change of w on the maximal profits assuming: p = 10, w = 1 and K = 100 Answer:

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Suppose that a producer has the following production function: Q = K³L'® Where Q is output, and L and K are man-hours and machine-hour the two inputs used in the production process. 1A) Set up the cost minimization problem as shown in class - In the cost minimization problem, the cost is minimized subject to constraint production function. It is indicated as follows: Minimize wL + rK subject to constraint Q = K3 L16 A = wL + rK + (Q-K-L6) The Lagrange f unction is differentiated by K andL to calculate the minimize the cost, and W= wage rate L=Labor R= real interest rate K = capital Q = output A= parameter coefficient 1B) Determine the cost-minimize ratio of inputs where capital costs $1 per machine-hour and labor costs $4 per lab- hour. - MRTS = Marginal product of labor Marginal product of capital Q = KL!6
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