Question

1. Suppose price-taking firms have cost functions given by C(q) = 90 + 5q + 0.025q .

1. What are the equations of marginal costs and average costs?

2. How much would the firm produce at prices of $9, $10, $11, and $12?

3. How much profit would the firm earn at prices of $9, $10, $11, and $12?

4. Graph the MC, AC. Indicate the profits at a price of $9 per unit.

5. What price would be charged in the perfect competitive equilibrium?

Explain answers.

Answer 1

The cost function is:C(q) = 90 + 5q + 0.025q^2

I think the question misses to put squared on 0.025q

Assume, the question is: C(q) = 90 + 5q + 0.025q^2

The marginal cost is MC(q) = dC/dq = 5 + 0.05q

The average cost is AC(q) = C(q)/q = 90/q + 5 + 0.025q

Since, the firm is price taker, equilibrium is given by P = MC

Thus, P = 5 + 0.05q

Thus, q at different prices of $9, $10, $11, and $12 are:

P	q
9	80
10	100
11	120
12	140

The Total Revenue at each price is given by: TR = Pq

TC = C(q) = 90 + 5q + 0.025q^2

Thus, the Profit = TR - TC

P	q	TR	TC	Profit
9	80	720	650	70
10	100	1000	840	160
11	120	1320	1050	270
12	140	1680	1280	400

Plotting MC and AC and profit at P=$9 is:

The marginal cost is MC = MC(q) = dC/dq = 5 + 0.05q

The average cost is AC=AC(q) = C(q)/q = 90/q + 5 + 0.025q

P	q	TR	TC	Profit	MC	AC
9	80	720	650	70	9	8.125
10	100	1000	840	160	10	8.4
11	120	1320	1050	270	11	8.75
12	140	1680	1280	400	12	9.142857

Th profit is highlighted by area in Green color.

The price that would be charged in the perfect comeptitive equilibrium is given by market condition and market forces of demand and supply. The firm is the price taker and has not influence on the price. In the long run, the price would be lower than $9 as there is short-run profit earned by the firm which will let free entry of the firms in the perfectly competitive market thereby providing downside pressure on the price such that in the long run each firm earns just a normal profit.