Please show all working. Find the amount of capital (K) and labour (L) that should be employed to maximizeoutput (q) given the following Cobb-Douglas production functions and constraintsset by Pk, PL and budget B:q(K,L) = K°ªL°6PK = 8, P, = 6, B = 300(You MUST justify that the stationary point you found does indeed maximizethe given function).

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Answered: Find the amount of capital (K) and…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 36CR

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A firm's demand function for a good is given by D: P= 100-2Q and their total cost function is given by TC = 300+8Q. Find the Quantity that maximizes the profit. O Q max = 26.05 O Q max = 2 O Q max = 4 O Q max = 23
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The production function for a firm is p(x, y) = 96x 3/4 1/4 y where x and y are the number of units of labor and capital utilized. Suppose that labor costs $144 per unit and capital costs $1875 per unit and that the firm decides to produce 24,000 units of goods. Determine the following. %3D ... 3/4 1/4 (a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 144x + 1875y, subject to the constraint 24,000 – 96x y = 0. X = , y= (Type exact answers in simplified form.)
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The production function for a firm is p(x, y) = 68x 3/4 1/4 y where x and y are the number of units of labor and capital utilized. Suppose that labor costs $102 per unit and capital costs $544 per unit and that the firm decides to produce 8704 units of goods. Determine the following. (a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 102x + 544y, subject to the constraint 8704 68x°7y' 3/4 1/4 = 0. x= 256 , y= 16 (Type exact answers in simplified form.) (b) Find the value of A at the optimal level of production. 1 = 4 (Type an exact answer in simplified form.) (c) Find the expressions for marginal productivity of labor and marginal productivity of capital. Then find the ratio of marginal productivity of labor to marginal productivity of capital at the optimum level of production and the ratio of unit price of labor to unit price of capital and determine the relationship between the…

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Find the amount of capital (K) and labour (L) that should be employed to maximize output (q) given the following Cobb-Douglas production functions and constraints set by Pk, PL and budget B: q(K,L) = K°ªL°6 Pg = 8,P, = 6,B = 300