Chapter 20: Problem 23

Which statement is false? \((\mathrm{LO} 4,5)\) a) \(\mathrm{AFC}\) plus \(\mathrm{AVC}\) equals \(\mathrm{ATC}\). b) Marginal cost equals AVC at an output of one. c) AVC equals ATC at an output of one. d) None is false.

Short Answer

Expert verified

The false statement is: c) AVC equals ATC at an output of one.

Step by step solution

Statement a: AFC plus AVC equals ATC

This statement suggests that Average Total Cost (ATC) is the sum of Average Fixed Cost (AFC) and Average Variable Cost (AVC). This is true because ATC takes into account both fixed and variable costs, and is calculated as: \[ \mathrm{ATC} = \frac{\mathrm{Total\ Fixed\ Cost}}{Q} + \frac{\mathrm{Total\ Variable\ Cost}}{Q} \] where Q is the quantity of output. Since \(\mathrm{AFC} = \frac{\mathrm{Total\ Fixed\ Cost}}{Q}\) and \(\mathrm{AVC} =\frac{\mathrm{Total\ Variable\ Cost}}{Q}\), we can combine them to get: \[ \mathrm{ATC} = \mathrm{AFC} + \mathrm{AVC} \] Thus, statement a is true.

Statement b: Marginal cost equals AVC at an output of one

Marginal cost (MC) is the cost of producing one additional unit of output. At an output of one, the marginal cost will be equal to the change in the total cost from producing zero units to producing one unit. On the other hand, the Average Variable Cost (AVC) is the total variable cost divided by the quantity of output. At an output of one, the Average Variable Cost will be equal to the total variable cost of producing just one unit. Since variable costs increase incrementally with each additional unit of production, it is highly likely that the cost of producing an additional unit at the output level of one (MC) will be equal to the cost of producing the first unit (AVC). Thus, statement b is true.

Statement c: AVC equals ATC at an output of one

At an output of one, the Average Variable Cost (AVC) is the total variable cost of producing just one unit, while the Average Total Cost (ATC) takes into account both fixed and variable costs. We know that: \[ \mathrm{ATC} = \mathrm{AFC} + \mathrm{AVC} \] At the output of one, the Average Fixed Cost (AFC) won't be zero, as the fixed costs are spread over the total output. Therefore, Average Total Cost (ATC) will be greater than the Average Variable Cost (AVC) at an output of one. This makes statement c false.

Statement d: None is false

Since we have already identified that statement c is false, statement d is also false because at least one statement is false. The false statement is: c) AVC equals ATC at an output of one.

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