Chapter 11: Problem 10

Sue's Surfboards rents a factory. If the rent rises by $\$ 200$ a week and other things remain the same, how do Sue's Surfboards' short-run average cost curves and marginal cost curve change?

Short Answer

Expert verified

SRATC and AFC increase, but MC remains unchanged.

Step by step solution

Understand the Cost Components

Divide the costs into fixed costs (rent) and variable costs (those that change with production). Sue's rent is a fixed cost.

Identify Short-Run Average Cost (SRAC)

Short-Run Average Cost (SRAC) is calculated as the total cost (fixed + variable) divided by the quantity of output. Increase in rent means an increase in fixed costs.

Impact on Average Fixed Cost (AFC)

Average Fixed Cost (AFC) is the fixed cost divided by the quantity of output. Since the fixed cost increased, the AFC will increase for all quantities of output.

Impact on Short-Run Average Total Cost (SRATC)

Short-Run Average Total Cost (SRATC) is the total cost divided by the quantity of output. With the increase in fixed costs, SRATC will increase at all levels of output.

Impact on Marginal Cost (MC)

Marginal Cost (MC) measures the change in total cost when the quantity produced changes by one unit. Since rent is a fixed cost, an increase in rent does not affect the marginal cost.

Conclusion

The increase in rent raises the Average Fixed Cost (AFC) and Short-Run Average Total Cost (SRATC) at all output levels, but the Marginal Cost (MC) remains unchanged.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

fixed costs

Fixed costs are expenses that do not change with the level of output produced. Examples include rent, salaries of permanent staff, and insurance payments. In Sue's Surfboards case, the rent for the factory is a fixed cost.

Fixed costs exist even if the production output is zero.
They are incurred regardless of the number of surfboards produced.
These costs are crucial for planning as they directly influence the average fixed cost and total cost calculations.
In the case of an increase in rent, Sue's fixed costs will rise, affecting the overall cost structure of the business.

variable costs

Variable costs change with the level of production. They include costs associated with materials, labor, and utilities that increase as more units are produced.

Examples of variable costs include:

Raw materials used in production.
Wages for temporary or hourly workers.
Utility costs like electricity and water, which rise with increased production activity.

For Sue's Surfboards, these costs might include materials for making surfboards or hourly wages for additional workers.

Understanding variable costs is essential for calculating the short-run average cost.

short-run average cost

Short-run average cost (SRAC) is the total cost divided by the quantity of output. SRAC combines both fixed and variable costs.

It is calculated as:
$ \text{SRAC} = \frac{\text{Total Cost}}{\text{Quantity of Output}} $

The total cost includes both fixed costs (like rent) and variable costs (like materials and labor).
An increase in fixed costs, such as a rise in rent, will increase the SRAC at all levels of output.
This is because even though the variable costs may remain the same, the higher fixed costs will push the average cost up.

average fixed cost

Average fixed cost (AFC) is calculated by dividing the fixed costs by the quantity of output produced.
Formula for AFC:
$ \text{AFC} = \frac{\text{Fixed Costs}}{\text{Quantity of Output}} $

Since fixed costs do not change regardless of the output, the AFC will decrease as production increases. However, with an increase in fixed costs like rent, the AFC will rise.
For Sue's Surfboards, if the rent increases, the AFC will be higher because the fixed cost has gone up.

short-run average total cost

Short-run average total cost (SRATC) includes both fixed and variable costs and is calculated as the total cost divided by the output quantity.
We can calculate it as:
$ \text{SRATC} = \frac{\text{Total Fixed Costs} + \text{Total Variable Costs}}{\text{Quantity of Output}} $

When fixed costs increase, such as a rise in rent, SRATC will increase as well because the total cost at each output level is higher.
For Sue's Surfboards, this means that the SRATC will be higher for all levels of output due to the increase in rent.

marginal cost

Marginal cost (MC) is the additional cost of producing one more unit of output. It is calculated by the change in total cost divided by the change in quantity.
Formula for MC:
$ \text{MC} = \frac{\Delta \text{Total Cost}}{\Delta \text{Quantity}} $

MC focuses on variable costs and does not include fixed costs since fixed costs do not change with output.
In Sue's scenario, an increase in rent, which is a fixed cost, will not affect the marginal cost because these costs are not seen in the calculation of the cost of producing additional units.
This means the marginal cost for producing each additional surfboard remains unaffected by the rent increase.

Sue's Surfboards rents a factory. If the rent rises by \(\$ 200\) a week and other things remain the same, how do Sue's Surfboards' short-run average cost curves and marginal cost curve change?