Question

You produce widgets. Currently you produce four widgets at a total cost of $$\$ 40$$. a. What is your average total cost? b. Suppose you could produce one more (the fifth) widget at a marginal cost of $$\$ 5 .$$ If you do produce that fifth widget, what will your average total cost be? Has your average total cost increased or decreased? Why? c. Suppose instead that you could produce one more (the fifth) widget at a marginal cost of $$\$ 20 .$$ If you do produce that fifth widget, what will your average total cost be? Has your average total cost increased or decreased? Why?

Short answer

Answer: The average total cost changes depending on the marginal cost of producing the additional widget. In scenario A, the average total cost decreases, while in scenario B, the average total cost increases.

Step-by-step solution

Calculate the initial average total cost

First, let's find the average total cost for producing four widgets. To do this, divide the total cost by the number of widgets produced, i.e. $$\frac{\$40}{4}$$.

Calculate the new total cost in scenario A

In scenario A, the marginal cost of producing the fifth widget is $$\$ 5$$. The new total cost would be the initial total cost plus the marginal cost: $$\$ 40 + \$ 5 = \$ 45$$.

Calculate the new average total cost in scenario A

To find the average total cost for producing five widgets in scenario A, divide the new total cost by the number of widgets produced: $$\frac{\$45}{5}$$.

Compare the average total cost in scenario A with the initial average total cost

Determine if the average total cost has increased or decreased in scenario A by comparing the results of Step 3 to Step 1.

Calculate the new total cost in scenario B

In scenario B, the marginal cost of producing the fifth widget is $$\$ 20$$. The new total cost would be the initial total cost plus the marginal cost: $$\$ 40 + \$ 20 = \$ 60$$.

Calculate the new average total cost in scenario B

To find the average total cost for producing five widgets in scenario B, divide the new total cost by the number of widgets produced: $$\frac{\$60}{5}$$.

Compare the average total cost in scenario B with the initial average total cost

Determine if the average total cost has increased or decreased in scenario B by comparing the results of Step 6 to Step 1.