A perfectly competitive firm fakes the following production function where Q is

Question

A perfectly competitive firm fakes the following production function where Q is the firm's output (in units) and L is the number of hours of tabor employed. The fir sells its output at a price of $6 per unit and it buys labor at the rate of $120 per hour. How many hours of labor should the firm employ? Justify your answer quantitatively, without calculating the level of profit. A firm is considering a capital investment that is expected to generate the following cash info at the end of each of the years indicated: The interest rate applicable to the loan that will be used to finance this investment project per year.

Explanation / Answer

If maximizing Q was the objective then using the given Q function

dQ/dL= 100 - L ; and d2Q/dL2=-1 which is <0 meaning L=100 is a maxima point

So if slope = dQ/dL = 0 then L=100

So the firm should employ 100 hours of labor for maximising Q.

However we need to maximize profit and not Q so profit function is given as:

P = 6Q - 120L = 6(50 + 100 L - 0.5L2) - 120L = 300 + 600 L - 3 L2 - 120 L

So, P = 300 + 480 L - 3 L2

Now we need to maximize P so using the equation for P obtained above,

dP/dL = 480 - 6L ; and d2P/dL2 = -6 which is less than 0 which means if dP/dL = 0; we obtain a value for L= 480/6 = 80 hours which is a point of maxima for maximizing P (profit function)

So in order to maximize profit the firm should employ 80 hours of labour

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