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

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ACME is a competitive firm producing magnetic birdseed with the following short-run cost function: TC = 0.1q2 ++10 0.2q + 1 The market price is $5. Find the following. Write your numerical answer(s) in the appropriate blanks. Do NOT include units or dollar signs. No fractions accepted-use decimals if needed. Do NOT round or truncate. Do NOT include any extra spaces or text. Show all work in your work file. a) profit maximizing output level: b) profit: c) average fixed costs: d) average variable costs: e) average total costs:

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a) Profit-maximizing output level: 20

ACME is a competitive firm producing magnetic birdseed.

ACME's short-run cost function is,

$TC = 0.1q^{2} + q + 10$

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

d(TC) / dQ = 0.2q +1

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

$\therefore MC = 0.2q +1$

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.

$\therefore$ 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

$\therefore$ 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

$\therefore$ 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

$\therefore$ 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

$\therefore$ 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,

$VC = 0.1q^{2} + q$

$\therefore AVC = (0.1q^{2} + q) / q$

Or, AVC = 0.1q + 1

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

AVC = 0.1 * 20 + 1

Or, AVC = 2 + 1

Or, AVC = 3

$\therefore$ 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

$\therefore$ Aaverage total cost = 3 + 0.5

Or, Average total cost = 3.5

$\therefore$ ACME's average total cost is 3.5

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

Economics