Question

In: Economics

Suppose the productivity of capital and labour are as shown in the accompanying table. The output...

Suppose the productivity of capital and labour are as shown in the accompanying table. The output of these factors sells in a perfectly competitive market for $1 per unit. Both capital and labor are hired under perfectly competitive conditions at $15 and $10, respectively.

K	MPK	L	MPL
0		0
1	30	1	21
2	27	2	18
3	24	3	15
4	21	4	12
5	18	5	9
6	15	6	6
7	12	7	3
8	9	8	1

a. What is the least‐cost combination of labour and capital the firm should employ in producing 96 units of output? Explain.

b. What is the profit‐maximizing combination of labor and capital the firm should use? Explain. What is the resulting level of output? What is the economic profit?

Expert Solution

A. Least cost combination for the output would be where the ratio of Marginal productivity to price is highest. Price is constant while the Marginal productivity decreases for both labor and capital as we hire more of those.

Since we have 2 different production factors with two different marginal products and prices, we can say that the least cost combination for the output would be where

MPK/P_K=MPL/P_L

We get

MPK/15=MPL/10

MPK/MPL=3/2.

Now we know that at optimal combination MPK and MPL are in a ratio of 3:2.

We also know that the output needs to be 96.

Going from the top, the first such combination is where MPK=27 and MPL=18 as 27/18=3/2.

At MPK=27, K=2 and production from capital=30+27=57.

At MPL=18, L=2 and production from labor=21+18=39.

Hence, total production=57+39=96.

Since the production is 96, we have out ideal combination. It is Capital=2 and Labor=2.

b. Profit maximizing combination will be where

MPK/P_K1 and MPL/P_L1.

What we are saying we will keep using capital till its extra utility per dollar is greater than or equal to 1. If the output from it on one dollar investment is lower than 1 dollar, there is no point in investing in it anymore. Same goes for labor.

Weve been given that P_K=15 and P_L=10. Hence, at profit maximizing output,

MPK15 and MPL10.

MPK equals 15 at 6. Labor becomes lower than 10 at 5 so we will stop at L=4, where MPL=12.

So the profit maximizing combination is 6 capital and 4 labor.

Output is

From Capital=30+27+24+21+18+15=135

From Labor=21+18+15+12=66

Total output=201.

Economic profit=Revenue-cost.

Revenue is 201 as price per unit is 1.

Cost is 6*15+4*10=90+40=130.

Economic profit=201-130=71.

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Rahul Sunny answered 1 hour ago

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