Question

Q. 2 Suppose that long- run average cost AC = 200 - 4Q + 0.05Q^2. What is the quantity at which AC is at a minimum? What is the value of AC and MC at this rate of production? What is the long- run equilibrium price?

Q. 3: The Burr Corporation's total cost function (where TC is the total cost in dollars and Q is quantity) is TC= 200 + 4Q+ 2Q^2 a. If the fi rm is perfectly competitive and the price of its product is $24, what is its optimal output rate? b. At this output rate, what is its profitt?

Q 4: The White Company is a member of the lamp industry, which is perfectly competitive. The price of a lamp is $50. The fi rm's total cost function is TC = 1,000 + 20Q + 5Q^2 where TC is total cost (in dollars) and Q is hourly output. a. What output maximizes profitt? b. What is the firm's economic profitt at this output? c. What is the firm's average cost at this output?

Answer 1

SOLUTION for Q.2:

Using the formula dAC/dQ= 0, the firms quantity at which AC is at a minimum :

AC = 200-4Q+0.05Q²

-4+0.1Q= 0

0.1Q= 4

0.1Q/0.1=4/0.1

Q=40

The value of AC and MC at this particular rate of production:

TC = AC *Q

TC = Q[200-4Q+0.05Q²]

TC = 200Q-4Q²+0.05Q³

MC= ∆TC / ∆Q

MC=200-8Q+0.15Q²

MC=200-8(40)+0.15(40)²

MC=200-320+240

MC=120

AC=200-4Q+0.05Q²

AC=200-4(40)+0.05(40)²

AC=200-160+80

AC=120

Therefore AC= $120 & MC = $120

MC = AC when the quantity Q=40

Since both the average and marginal costs of the firms are equal at quantity Q = 40, the long run equilibrium cost of the firm also remains to be $120.

SOLUTION for Q.3:

a) A point at which the price of the firm equals to its marginal cost is said to be its optimal output rate.

TC = 200+4Q+2Q²

since the firm is said to be a perfectly competitive firm we must use the rule P=MC inorder to find the optimal output rate.

MC = 4+4Q

4+4Q = 24

4Q     = 24-4

4Q    = 20

The optimal output rate Q = 5.

b) The profit of the firm at this level of output:

   TR= P × Q

   TR= 5 × 24

   TR = $120.

SOLUTION for Q.4:

a) MC = 20+10Q

From the above statement it is given that the White company is perfectly competitive, then we are supposed to use

P= MC rule to find the optimum level of quantity that would maximise the profit of the firm. That is

20+10Q= 50

10Q = 50-20

Q= 30/10

Thus, Q= 3 . It is also observed that the marginal cost function is an increasing function of Q and seems to be a straight line with a positive slope of 10. Henceforth, the optimum quantity maximizing the firms profit is Q= 3.

b)Profit = TR(Q=3)-TC(Q=3)

           = 50(3)-[1000+20(3)+5(3)2]/3

           = -$955

Therefore the firms economic profit at this level of output is -$955.The firm is experiencing big loss in relation to its revenues and as a result the industry could not retain its position in the state of equilibrium.

c)The firms average total cost ATC at this level of output :

ATC = [1000+20(3)+5(3)2]/3

             = $368.33 .