A firm hires the number of capital and labor according to its productivity . The

Question

A firm hires the number of capital and labor according to its productivity . The firm need a combination of one unit of capital and two units of labor per hour to make ten units of output. The technology is such that an increase in labor has to be accompanied with an increase in capital, and a decrease in labor has to be accompanied with decrease in capital in the same proportion for the firm to maximize profits. Price per labor is $8 and price per unit of capital is $10. The price of the product is $5 per unit of output.

a.) how do you find the equation to the isocost line?
b.) Now if you were to assume that the firm has to produce 1000 units to maximize profits. How do you find the combination of labor and capital that firm would need? And how do you find what the total cost would be? Also, how much is the profit?

Explanation / Answer

a) isocost equation is, rK + wL = C where r is cost of capital= $10 per unit, K is amount of capital, w is cost of labour per unit = $8, L is amount of labour and C is total cost of inputs. so, isocost eqn. in this case is, 10K + 8L = C (ANSWER) b) for 1000 output, K = (1000/10)*(capital per 10 units of output) = 100*1=100 units and L = (1000/10)*(labour per 10 units of output) = 100*2 = 200 units C = 10*100 + 8*200 = 2600 ($) (ANSWER) Profit = Revenue - cost = 5*1000 - 2600 = 5000 - 2600 = 2400 ($) (ANSWER)

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