Columns 1 and 2 make up a portion of a monopolist's production function for a single variable input,labor.Columns 2 and 3 represent the demand function facing the monopolist over this range of output: If an increase in consumers' income increases product price by $2 at each level of output,how many units of labor will the firm employ at a wage rate of $300?

Question

Columns 1 and 2 make up a portion of a monopolist's production function for a single variable input,labor.Columns 2 and 3 represent the demand function facing the monopolist over this range of output:  If an increase in consumers' income increases product price by $2 at each level of output,how many units of labor will the firm employ at a wage rate of $300?

Quizplus · Accepted Answer

To determine the optimal level of labor for a given wage rate and output level, we need to find the point where the marginal cost of labor equals the marginal revenue product of labor.

At a wage rate of $300, the marginal cost of labor equals $300. To find the marginal revenue product of labor, we need to calculate the derivative of total revenue with respect to labor, which is equal to the marginal revenue from column 2 multiplied by the quantity sold at each level of output from column 3, or:

MRPL = (10-0.1L)*1100

Setting MRPL equal to MC, we get:

(10-0.1L)*1100 = 300
=> L = 50/11

However, this is not a feasible solution since the firm can only employ integer units of labor. We therefore round down to the nearest integer, which gives:

L = 4

Therefore, the firm will employ 4 units of labor at a wage rate of $300.

Columns 1 and 2 Make Up a Portion of a Monopolist's