ACME is a competitive firm producing magnetic birdseed with the following short-run cost function: TC = 0

Answer

a) Profit-maximizing output level: 20

ACME is a competitive firm producing magnetic birdseed.

ACME's short-run cost function is,

Differentiating the above cost function with respect to Q, we get,

The above expression shows ACME's marginal cost(MC) function.

The market price is $5.

The firm is the price taker in the market. So its marginal revenue, i.e., change in total revenue for the sell of an additional unit of output, equals the market price.

 MR = Price = $5

We know that a firm produces the profit-maximizing level of output, at which, the marginal cost of the firm equals the marginal revenue(MR), i.e., MC = MR

 0.2q + 1 = 5

Or,  0.2q = 5 - 1

Or,  0.2q = 4

Or, q = 4 / 0.2

Or, q = 20

So, the firm's profit-maximizing level of output is 20 units.

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b) Profit: 30

Profit = Total Revenue - Total Cost

Total Revenue = Price * Quantity

 ACME's Total Revenue = $5 * 20 = $100

Or,  ACME's Total Revenue = 100

Now, if we put, q = 20 in ACME's total cost function, we get,

TC = 0.1 * 20 * 20 + 20 + 10

Or, TC = 40 + 20 + 10

Or, TC = 70

 ACME's Profit = 100 - 70 = 30

So, ACME's profit is 30.

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c) Average fixed costs: 0.5

Average fixed cost = Total fixed cost / Output

From ACME's total cost function, we see that its fixed cost is, 10, which is independent of output(q).

ACME's output(q) = 20

   Average fixed cost = 10 / 20 = 0.5

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d) Average variable costs:  3

Average variable cost = Variable cost(VC) / Output

From ACME's total cost function, we see that its average variable cost(AVC),which depends on the output(q), is,

Or, 

Now, putting q = 20 in the above equation, we get,

Or, 

Or, 

 ACME's average variable cost is 3

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e) Average total costs: 3.5

Average total cost(ATC) = Average variable cost + Average fixed cost

 Aaverage total cost = 3 + 0.5

Or,  Average total cost = 3.5

 ACME's average total cost is 3.5