Suppose that labor is the only input used by a perfectly...

Suppose that labor is the only input used by a perfectly competitive firm. The firm's production function is as follows: a. Calculate the marginal product for each additional worker. b. Each unit of output sells for \$10. Calculate the value of the marginal product of each worker. c. Compute the demand schedule showing the number of workers hired for all wages from zero to \$100 a day. d. Graph the firm's demand curve. e. What happens to this demand curve if the price of output rises from \$10 to \$12 per unit?

Suppose that labor is the only input used by a perfectly competitive firm. The firm's production function is as follows:

a. Calculate the marginal product for each additional worker.
b. Each unit of output sells for \$10. Calculate the value of the marginal product of each worker.
c. Compute the demand schedule showing the number of workers hired for all wages from zero to \$100 a day.
d. Graph the firm's demand curve.
e. What happens to this demand curve if the price of output rises from \$10 to \$12 per unit?

Key Concepts

Production Function

The production function defines the relationship between inputs (in this case, labor) and the output produced by a firm. It encapsulates the technological process of converting inputs into goods or services and is fundamental for analyzing how changes in input levels affect production levels.

Marginal Product of Labor

The marginal product of labor refers to the additional output produced by employing one more unit of labor. It is a critical concept for understanding the productivity of workers and plays a key role in decision-making regarding how many workers to hire.

Value of the Marginal Product

The value of the marginal product is obtained by multiplying the marginal product by the price of the output. It represents the additional revenue generated by employing one extra worker and serves as an essential criterion for hiring decisions in a competitive market.

Labor Demand Schedule

The labor demand schedule outlines the relationship between the wage rate and the quantity of labor demanded by a firm. It is derived by equating the value of the marginal product of labor to the wage, showing how many workers are hired at different wage levels.

Perfect Competition in Labor Markets

In a perfectly competitive market, firms are price takers for both the output they sell and the labor they hire. This means that the firm cannot influence the market price of its output or wages, and decisions regarding employment are based solely on marginal analysis, such as comparing the wage to the value of the marginal product.

Transcript

00:01 In question three, we have this following chart of the firm's production function.

00:07 So question a, calculate the margin product for each additional worker.

00:13 So this is the most basic question.

00:16 So we just have to see that, okay, from zero to one, so the days of labor here means that each day they hire one more labor.

00:27 So from day zero to day one, they hire this one more labor, which produced seven units of output.

00:37 So the marginal product for this first labor is seven.

00:45 So from day one to day two, this second labor produced six extra units because 13 minus seven is six.

00:55 Okay.

00:56 So the third labor produced 19 minus 13, which is also 6.

01:05 And then the fourth labor produced 25 minus 19, which is also 6.

01:14 And then the fifth labor produced three extra units.

01:21 And then the 6th labor produced only one unit.

01:26 And what about hiring the seven? the seven labor produce nothing.

01:35 So maybe all the resources are already used up.

01:38 That's why this last labor does not contribute anything.

01:44 Okay, question b, each unit of output sells for $10.

01:49 So calculate the value of the marginal product of each worker.

01:54 So all the blue numbers here are the marginal product.

02:00 So what about the value of marginal product? the value of marginal product of labor is just the price of the quantity they produce times this marginal product of labor.

02:21 Okay, so here, so i will just time...

02:31 Times 10.

02:33 So the value of margin of labor is just 70 for the first labor and then 60 for the second labor and also 60.

02:43 So all this column on the left and side times by 10.

02:48 Okay, so 70, 60, 60...

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