Answer to Question #228155 in Macroeconomics for BROTHER

Question

Describe how firms determine the optimum amount of the variable input and the best

stage of production in a short run production function. Give an adequate justification

mathematically and graphically

Answer 1

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Given that the capital input, or any input in general, is fixed, a firm can use information on product pricing and factor costs to calculate the optimal quantity of the variable input to use. This includes a discussion of MRP (marginal revenue product) and MFC (marginal factor cost).

MRP

This is defined as the increase in total revenue resulting from the use of an extra unit of the variable factor, or assume that the variable input is labor. The marginal product of labor times the marginal revenue from selling the additional units of output will equal the change in total revenue. The marginal revenue from additional units will be constant if the firm is operating under the conditions of perfect competition.

MFC

This is defined as the cost of adding an additional unit of the variable element to the total cost.

illustration:

Consider the following short run production function L=variable input Q= output Q=10L-0.5L^2. Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input as it needs at $20 per unit.

A. Determine marginal revenue product function

B. determine marginal factor cost function

C. Determine the optimal value of L, given the objective is to maximize profits

SOLUTION

$A. Marginal \ revenue \ product\ function is:\\ MRP = MR*MP = 10*Q' = 100 - 10L\\ B. Marginal factor\ cost \ function\ MC = Q' = 10 - L\\ C. The\ optimal \ value \ of\ L, given \ the\ objective \ is \ to\ maximize\ profits, \\ is \ when \ MRP = 0, so \ 100 - 10L = 0, L = 10,\\ therefore\ 10\ workers \ should\ be \ hired\ to\ maximize \ profits.$

Hence the best stage of production in the short run is where there occurs that profit is maximized(at profit maximization level) .