Question

The company uses in the production of commodity X two independent resource A and B (labor and capital). measure of marginal products of resources are shown in the table below. goods are sold at a price of 50 thousand dollars.

Qa MPa Qb MPb
1 12 1 20
2 11 2 18
3 10 3 16
4 9 4 14
5 8 5 12
6 6 6 10
7 5 7 8
8 3 8 6


Determine the following: At what proportion of resources firm maximizes profit if PA= $250 and PB= $400., and what is the size of the profits.

Answer 1

resource A and B (labor and capital).

$\mathrm{Px} = \$50$

Determine the following: At what proportion of resources firm maximizes profit if PA= $250 and PB= $400., and what is the size of the profits.

Solution:

We can find maximized profit from the formula:

$$\mathrm{TP} = \mathrm{TR} - \mathrm{TC} = \mathrm{Pa} \cdot \mathrm{q} - (\mathrm{PA} + \mathrm{PB}) = \max$$

Value of marginal products of labor and capital should be equal to their wages and rental rate respectively, so:

$\mathrm{Px} \cdot \mathrm{MPa} = \mathrm{PA}, 50 \cdot \mathrm{MPa} = 250, \mathrm{MPa} = 5,$

$\mathrm{Px} \cdot \mathrm{MPb} = \mathrm{PB}, 50 \cdot \mathrm{MPb} = 400, \mathrm{MPb} = 8$, so we see from the table, that $q = 7$

Now we can calculate maximizing profit:

$\mathrm{TP} = 50 \cdot 7 - (250 + 400) = -300$ thousand dollars.

So, there is a loss, that is minimized.