Question

Consider a perfectly competitive market in which each firm's short-run total cost function is C= 81 +9q+q^2, where q is the number of units of output produced. The associated marginal cost curve is MC = 9 + 2q.

In the short run each firm is willing to supply a positive amount of output at any price above $_________ (Enter your response as a real number rounded to two decimal places.)

If the market price is $27, each fim will produce ________ units in the short-run. (Enter your response as a real number rounded to one decimal place.)
Each firm earns a profit of $_________ . (Enter your response as a real number rounded to two decimal places, and use a negative sign if the firm has a loss rather than a profit). In the long run, firms will ________ the industry Suppose the short-run cost function given above [C= 81+9q+q^2] is the one that all firms would use in the long-run, because the corresponding 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. (Enter your response as a real number rounded to one decimal place.)

Answer 1

Answer:

above $11

They will produce 9 units

the economic profit will be of zero at equilibirm

the firm will stay as they are achieving economic gains

in the long run the firms will produce 6.36 units

Explanation:

To find equilibriuem we qualize marginal revenue (slaes price) and marginal cost)

To produce at least 1 unit (positive outcome)

the companies will need when, q = 1 at a price of:

MR = MC

MR = 9 + 2(1) = 11

if the market price is $27 then:

27 = 9 + 2Q

(27-9)/2 = Q

Q = 9

27 x 9 - (81-9(9)+9^2)

243 - (81 + 81 + 81) = 243 - 243 = 0

In the long-run the company will produce when average cost matches marginal cost

Average cost = Marginal Cost

(81 + 9q + q^2)/q = 9+2q

81 + 9q = (9 + 2q)*q

81 + 9q = 9q + 2q^2

-2q^2 + 81 = 0

We solve with the quadratic formula to get the roots

q = 6.36