Hello, I was hoping someone could help me with the following questions... Q: Sup

Question

Hello, I was hoping someone could help me with the following questions... Q: Suppose that there are 20 identical firms in the bolt-making market, a perfectly competitive market. Each firm has short-run total cost function TC(q) = 16 + q2, where q is the annual output of the firm. The corresponding short-run marginal cost function is MC(q) = 2q. The market demand for bolts is QD = 110 – P, where P is the market price. - (a) Find the short-run competitive supply curve. - (b) Find the short-run competitive equilibrium price and quantity for this market. - (c) How much does each individual firm produce in equilibrium? What is each firm’s profit? - (d) Find total market producer surplus. - (e) Find total market surplus.

Explanation / Answer

TC(q) = 16 + q2

MC(q) = 2q

QD = 110 – P

P = 110 - QD

(a) Find the short-run competitive supply curve

Short supply curve for each firm is it's MC curve , P= 2q

So, Industry Supply Curve = P = 2q/20 = q/10 or q = 10P

(b) Find the short-run competitive equilibrium price and quantity for this market. -

For, short-run competitive equilibrium,

Qd = Qs

110 - P = 10P

P = 110/11 = 10

Q = 110 - 10 = 100

  

(c) How much does each individual firm produce in equilibrium?

Each firm , q = P/2 = 10/2 = 5

What is each firm’s profit?

Profit = TR -TC = P*q - 16 - q2 = 10*5 - 16 - 5^2 = 50 - 41 = 9

- (d) Find total market producer surplus.

= 1/2(10-0)(100)

= 500

- (e) Find total market surplus.

Consumer Surplus = 1/2(110-10)*100

= 5,000

If you don't understand anything, then comment, I will revert back on the same.

And If you liked the answer then please do review the same. Thanks :)

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