Question

1.a. A competitive firm has a short run total cost curve represented by the following equation:

C(q) = 50 + .05q2

Derive the marginal cost. Derive the expressions for average total cost and average variable cost for this C(q)

b. In the short run, if the price is $4, what is marginal revenue? How many units should a profit maximizing competitive firm produce? What is its profit (loss)? Would this firm produce in the short run (long run) at this price? If the price is $20, how many units does a firm produce? What is its profit or loss?

c. What is the firm's short run supply curve (an equation: qs=)? Hint: how did you know how many units the firm produces at each price?

d. If there are 50 identical firms in this market, what is the supply curve? If the market demand Qd= 5000-500P, what is the amount sold and the market price? What do profits for the individual firm equal?

e. What happens in the long run?

Please answer all parts

Answer 1

1.(a) C(q)= 50 + 0.05q²

Marginal cost=

= 0+0.1q

Thus, Marginal cost = 0.1q

Average total cost =

=(50 + .05q²) / q

Thus, Average total cost =50/q + 0.05q

Average variable cost = Variable cost / q

= 0.05q² / q

Thus, Average variable cost = 0.05q

(b)Market price = $4

Therefore, Marginal Revenue = $4

Profits are maximised when price = marginal cost

i.e 4= 0.1q

q= 40

Profit = Total revenue - Total cost

Total revenue = $4*40=$160

Total cost = 50 + .05q² = 50 +0.05(40²) = $130

Profit   = 160 - 130

Profit   = $30

A firm will produce in the short run only if its revenue is greater than its total variable cost.

The firm's short run supply curve is its MC curve above minimum AVC

AVC= 0.05q

MC= 0.1q

i.e MC>AVC and the firm would produce in short run as long as p>0

When price= $20,

Profits are maximised when price = marginal cost

i.e 20= 0.1q

q= 200

Profit = Total revenue - Total cost

Total revenue = $20*200=$4000

Total cost = 50 + .05q² = 50 +0.05(200²) = $2050

Profit   = 4000- 2050=1950

Therefore, when price - $20, q= 200 and Profit   = $1950

(c)The firm produces output as long as P=MC and MC   AVC.

We have  MC= 0.1q always greater than AVC= 0.05q.

So, the entire marginal cost curve is the supply curve. Therefore, P=0.1q or Q_S=10 p is the firm's short run supply curve.

(d) Q_S=10 p

There are 50 identical firms in the market. So, short-run market supply equals 50 *Q_S= (50* 10P) =500P

When there are 50 identical firms, Q_S=500P

Q_d= 5000-500P

The short-run equilibrium occurs where market supply equals market demand.

5000-500P =500P

   1000P=5000

P= 5

Market price = $5

Substituting P=5 in supply curve, we get 500P = 500*5=2500

i.e Amount sold  = 2500

Economic profit in the short-run = Total Revenue - Total cost

Total Revenue (price times the short-run quantity supplied by each individual firm ) = T R = P ∗ q

T R = 5*50 = 250

Total cost (short-run total cost curve) = TC = 50 + .05q²

= 50+ 0.5*50*50

= 1300

Economic profit in the short-run =⇒ = 250 - 1300

= -1050

Therefore, firms will make negative short-run profit.

(e) In the long-run, each firm’s economic profit will be zero.