Suppose that for the firm below, the goods market is perfectly competitive. The market price of the product the firm produces is $4 at each quantity supplied by the firm. What is the amount of labor that this profit-maximizing firm will hire, and what wage rate will it pay?

Labor Supplied Total Physical Product Hourly Wage Rate($)
10 100 5
11 109 6
12 116 7
13 121 8
14 124 9
15 125 10

what is the answer to this????

To determine the amount of labor that the profit-maximizing firm will hire and the wage rate it will pay, we need to consider the firm's production and cost. The firm aims to maximize its profit, which is the difference between total revenue and total cost.

First, let's calculate the firm's total revenue (TR). In a perfectly competitive market, the firm will sell its output at the market price, which is $4 in this case. The total revenue can be calculated by multiplying the market price by the quantity supplied:

TR = Market Price * Quantity Supplied

Next, we need to calculate the firm's total cost (TC). For a profit-maximizing firm, the cost of labor is an important factor. The total cost can be calculated by multiplying the amount of labor hired by the wage rate:

TC = Labor Hired * Hourly Wage Rate

Now, let's calculate the total revenue and total cost at each level of labor supplied:

Labor Supplied | Total Physical Product | Hourly Wage Rate($) | Total Revenue | Total Cost
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10 | 100 | 5 | TR = $4 * 100 | TC = $5 * 10
11 | 109 | 6 | TR = $4 * 109 | TC = $6 * 11
12 | 116 | 7 | TR = $4 * 116 | TC = $7 * 12
13 | 121 | 8 | TR = $4 * 121 | TC = $8 * 13
14 | 124 | 9 | TR = $4 * 124 | TC = $9 * 14
15 | 125 | 10 | TR = $4 * 125 | TC = $10 * 15

Now, compare the total revenue and total cost at each level of labor supplied. Identify the quantity of labor where the difference between total revenue and total cost is highest. This will be the profit-maximizing level of labor.

Finally, identify the wage rate corresponding to the profit-maximizing level of labor. This will be the wage rate that maximizes the firm's profits.

Based on these calculations, the profit-maximizing firm will hire 14 units of labor and pay a wage rate of $9.