The total cost of producing 10 dollhouses is $2100, of which $100 is fixed. Producing the 11th dollhouse will cost $120. Which of the following are true? Note: this question has between 1 and 4 correct answers: you will receive partial credit for each correct answer (but will lose points for each incorrect answer given).

Question

BlackTom AI · Accepted Answer

First, I’ll lay out the key numbers we’re working with for clarity.
- Total cost for 10 units (TC10) = 2100, Fixed cost (FC) = 100, so Variable cost (VC) for 10 units = 2100 − 100 = 2000.
- Average total cost at 10 units (ATC10) = 2100 / 10 = 210.
- Average variable cost at 10 units (AVC10) = 2000 / 10 = 200.
- Average fixed cost at 10 units (AFC10) = 100 / 10 = 10.
- Cost to produce the 11th unit (MC11) = 120, so TC11 = 2100 + 120 = 2220 and ATC11 = 2220 / 11 = 202.
With these calculations in mind, evaluate each statement:

Option 1: The average total cost of producing 11 units is $200.
Here, ATC11 = 202, not 200, so this statement is false. The math shows ATC rises slightly from 210 at 10 units to about 202 at 11 units, but it does not equal 200.

Option 2: The average variable cost of producing 10 units is $200.
This is exactly AVC10 = 200, based on VC10 = 2000 divided by 10 units. This statement is true.

Option 3: The average fixed cost of producing 10 units is $10.
AFC10 = FC / 10 = 100 / 10 = 10. This matches the calculation, so the statement is true.

Option 4: The firm would have to shut down if the price was $210.
Shutdown decision depends on price relative to AVC. Since AVC at 10 units is 200, and the price 210 > 200, the firm would not shut down; it would continue producing in the short run. Therefore, this statement is false.

In summary, options 2 and 3 are true, while options 1 and 4 are false.

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