Ball Bearings Inc is a single producer in the ballbearing ma

Ball Bearings, Inc. is a single producer in the ball-bearing market, which is a perfectly competitive. The firm’s costs of product is provided in the table below:

a. Fill in the table above by making the appropriate calculations.

The variable q represents the firm\'s output, VC is the firm\'s variable cost, and TC is the firm\'s total cost.

b. In the table below, write the optimal quantity of output for the firm at each of the prices (column 1); indicate whether the firm should shut down or produce in the short run (column 2); provide a brief justification for your answer in column 2 (column 3); indicate whether the firm would exit or remain in the market over the long term (column 4); provide a brief justification for your answer in column 4 (column 5).

Price

Optimal Quantity

Shutdown/

Produce

Brief explanation of (2)

Exit/

Remain

Brief explanation of (4)

1

2

3

4

5

$20

$30

$40

$60

c. Suppose the firm imposed a $10 per unit tax on each unit produced. If the market price is $40 what is the firm\'s optimal quantity of output? Would they produce or shut down in the short run? Would they remain in the market or exit in the long run? Justify your answer.

Solution

(a)

Working notes:

(1) AVC = VC / q

(2) TC = TC / q

(3) MC = Change in TC / Change in q

(b)

Working notes:

(1) A perfect competitor maximizes profits (minimizes losses) when Price = MC.

(2) In short run, a firm will produce (shut down) if Price is higher than (lower than) AVC.

(3) In long run, a firm will stay (exit) if Price is higher than (lower than) ATC.

(c)

The $10 tax will increase AVC, ATC and MC by $10 at every output level.

When Price = MC = $40, optimal quantity = 3 units. At this price-output combination, Price equals AVC, therefore firm is indifferent between shutting down or producing. But since Price is less than ATC at this level, firm will exit the market in long run.