Question

In the short run, a tool manufacturer has a fixed amount of capital. Labor is a variable input. The cost and output structure that the firm faces is depicted in the following table. Suppose that for the firm, the goods market is perfectly competitive. The market price of the product is $5 at each quantity supplied by the firm. Labor Supplied | Total Physical Product | Hourly Wage Rate ($) | Total Wage Cost | Marginal Factor Cost 10 | 100 | 5 | 50 | - 11 | 109 | 7 | 77 | 27 12 | 117 | 9 | 108 | 31 13 | 124 | 11 | 143 | 35 14 | 130 | 13 | 182 | 39 15 | 135 | 15 | 225 | 43 What is the amount of labor that this profit-maximizing firm will hire? workers. (Enter a numeric response using an integer.)

          In the short run, a tool manufacturer has a fixed amount of capital. Labor is a variable input. The cost and output structure that the firm faces is depicted in the following table.
Suppose that for the firm, the goods market is perfectly competitive. The market price of the product is $5 at each quantity supplied by the firm.
Labor Supplied | Total Physical Product | Hourly Wage Rate ($) | Total Wage Cost | Marginal Factor Cost
10 | 100 | 5 | 50 | -
11 | 109 | 7 | 77 | 27
12 | 117 | 9 | 108 | 31
13 | 124 | 11 | 143 | 35
14 | 130 | 13 | 182 | 39
15 | 135 | 15 | 225 | 43
What is the amount of labor that this profit-maximizing firm will hire? workers. (Enter a numeric response using an integer.)

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In the short run, a tool manufacturer has a fixed amount of capital. Labor is a variable input. The cost and output structure that the firm faces is depicted in the following table.
Suppose that for the firm, the goods market is perfectly competitive. The market price of the product is 5 at each quantity supplied by the firm.
Labor Supplied | Total Physical Product | Hourly Wage Rate () | Total Wage Cost | Marginal Factor Cost
10 | 100 | 5 | 50 | -
11 | 109 | 7 | 77 | 27
12 | 117 | 9 | 108 | 31
13 | 124 | 11 | 143 | 35
14 | 130 | 13 | 182 | 39
15 | 135 | 15 | 225 | 43
What is the amount of labor that this profit-maximizing firm will hire? workers. (Enter a numeric response using an integer.)

Added by Emily S.

Principles of Economics

Gregory Mankiw 8th Edition

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Solved by Expert Andrew Davis

08/09/2023

Step 1

In a perfectly competitive market, the firm's marginal revenue is equal to the market price, which is $5 in this case. Show more…

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In the short run, a tool manufacturer has a fixed amount of capital. Labor is a variable input. The cost and output structure that the firm faces is depicted in the following table: Labor Supplied 10 11 12 13 14 15 Total Physical Product 100 109 117 124 130 135 Hourly Wage Rate ($) 5 7 9 11 13 15 Total Wage Cost 50 77 108 143 182 225 Marginal Factor Cost - 27 31 35 39 43 Suppose that for the firm, the goods market is perfectly competitive. The market price of the product is $5 at each quantity supplied by the firm. What is the amount of labor that this profit-maximizing firm will hire? (Enter a numeric response using an integer.)

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Transcript

00:01 So here we're talking about production, right, and we're thinking about how many firms, the workers the firm will hire.

00:06 Now the firm wants to maximize profit, and you may have seen profit maximization expressed by marginal revenue equals to marginal cost before.

00:17 But here the marginal cost of a laborer, of a worker, is just their wage.

00:21 It's how much you pay them, right? and the marginal revenue, however, is the price times the marginal product of labor.

00:30 So this here is the cost of a worker, and this here is the value of a worker.

00:35 And so the firm wants to hire workers as long as the value is greater than the cost for the marginal worker.

00:46 So here we have, let me marginal cost.

00:59 So we are given, let's say, 10 and 11, 100, 109.

01:08 Oh sorry, this is the total product, not the marginal product.

01:13 So what i'm going to do is construct a new column, the marginal product.

01:17 Here, as we increase, the marginal product is 9, and we know, we're told that the price is equal to 5.

01:25 So the price times the marginal product of labor is 45, right? so the wage is, here, is 5 and 7.

01:38 The total cost is 50 and 77.

01:42 The marginal cost is 27.

01:44 So if we compare these two, you see it's a good idea...

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