Question

Consider a perfectly competitive market in which each​ firm's short-run total cost function is C​ = 64 + 6q ​+ q²​, where q is the number of units of output produced.

The associated marginal cost curve is MC​ = 6​+ 2q.

In the short run each firm is willing to supply a positive amount of output at any price above ___.

If the market price is ​$30 each firm will produce ____ units in the​ short-run.

Each firm earns a profit of ___.

Suppose the short-run cost function given above is the one that all firms would use in the long-run, because the corresonding SAC curve is tangent to the LAC curve at the minimum point on the LAC curve. In the long run, each firm will produce ___ units.

Answer 1

Cost function is C​ = 64 + 6q ​+ q²​ where AC = 64/q + 6 + q and MC​ = 6​+ 2q. Also AVC = 6 + 2q

In the short run each firm is willing to supply a positive amount of output at any price above $6. This is because it is minimum of AVC which represents the shut down price.

If the market price is ​$30 each firm will produce 12 units in the​ short-run. This is because firm will use P = MC to find how much to produce. This gives 2q = (30 - 6) or q = 24/2 = 12 units.

Each firm earns a profit of $80. This is because revenue is 12*30 = 360 and cost is 64+6*12+12^2 = 280. Hence profit is 360 - 280 = $80

Now AC is minimum when AC'(q) = 0

-64/q^2 - 1 = 0

q = 8

In the long run, each firm will produce 8 units.