Suppose that the productivity of capital and labour are as shown in the table be
ID: 1194614 • Letter: S
Question
Suppose that the productivity of capital and labour are as shown in the table below. The output of these factors sells in a perfectly competitive market for $1 per unit. Both capital and labour are hired under perfectly competitive conditions, and the price of capital is $3 per unit, while the price of labour is $1 per unit.
a. [3 points] Calculate the marginal product of capital divided by the price of capital (MPC/PC), and the marginal product of labour divided by the price of labour (MPL/PL), and add these to the table above. What is the least-cost combination of labour and capital the firm should employ if the firm wants to produce 80 units of output? Explain.
b. [3 points] Calculate the marginal revenue product of capital divided by the price of capital (MRPC/PC), and the marginal revenue product of labour divided by the price of labour (MRPL/PL), and add these to the table above. What is the profit-maximizing combination of labour and capital the firm should use? Explain. What is the resulting level of output? What is the economic profit?
Units of Marginal MPoPcMRPo Pc Units of Marginal MP/PMRPL/PL. Capital Product of LabourProduct of Capital 24 21 18 15 Labour 9 4 4 4Explanation / Answer
a)MPC/PC MPL/PL
8 11
7 9
6 8
5 7
3 6
2 4
1 1
0.33 0.5
a)C=2,L=4 units, the ratios are equal to 7 for each.The least-cost combination is found by equating the ratios of the marginal products of each input to their prices.
b)7 capital and 7 labor,Output is 142 (= 96 from capital + 46 from labor). Economic profit is $114 (= $142 - $28). Yes, least-cost production is part of maximizing profits. The profit-maximizing rule includes the least-cost rule
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