Question

Suppose that for a particular firm the only variable input into the production process is labor and that output equals zero when no workers are hired. in addition, suppose that fixed cost is $130, marginal cost of each worker hired is constant at $40, and the average total cost when three workers are hired is $50. what is the output when three workers are hired?

Answer 1

The output when three workers are hired for the firm is 13 units.

Step-by-step explanation:

The marginal cost of each worker hired is constant at $40. The average total cost when three workers are hired is $50. To find the output when three workers are hired, we can use the relationship between marginal cost (MC), average total cost (ATC), and output. Since MC equals ATC at the minimum point of the ATC curve, we know that the output when three workers are hired is the same as the output at the minimum point of the ATC curve. Therefore, to find the output when three workers are hired, we need to find the minimum point of the ATC curve.

Let's assume that the output when three workers are hired is Q units. The total cost (TC) of producing Q units can be calculated using the formula:

TC = FC + (MC * Q)

Given that the fixed cost (FC) is $130, the marginal cost (MC) is $40, and the average total cost (ATC) when three workers are hired is $50, we can set up the equation:

$130 + ($40 * Q) = $50 * Q

Simplifying the equation:

$130 + $40Q = $50Q

$10Q = $130

Q = $130 / $10

Q = 13

Therefore, the output when three workers are hired is 13 units.

Answer 2

The output when three workers are hired is 5 units. This was calculated using the average total cost for three workers, the fixed cost, and the constant marginal cost per worker.

Step-by-step explanation:

To determine the output when three workers are hired, we need to use the information on average total cost (ATC) and fixed cost. Given a fixed cost of $130 and a constant marginal cost of $40 per worker, if the ATC is $50 when three workers are hired, we can calculate the total cost (TC) and subsequently the output (also known as total product or TP).

Firstly, we determine TC for three workers:

Where Q is the output.

We also know that TC is the sum of total variable cost (TVC) and total fixed cost (TFC):

Substituting the TC value back into the ATC equation, we get:

Therefore, the output when three workers are hired is 5 units.