Question

Suppose that the wheat market in Ghana is a perfectly competitive one where all the firms are identical with identical cost curves. Again, suppose that a single firm’s total cost (TC) function is given as TC = 100 + q2 + q where q is the quantity of output produced by the firm. Furthermore, the market demand function for this product is given by the equation Q = 500 – 0.5P, where Q is the market quantity demanded. Also, the market supply function is given by the equation q = -100 + P.
You are required to provide answers to the following questions:
(a)     Calculate the equilibrium quantity and price in this market given the above information?

(b)     Determine the firm’s,
       i. profit maximising level of production,     6 marks
ii. profit at this market equilibrium.    
v. Is this a short-run or long-run equilibrium? Explain your answer.     
(c)     Given your answer to question (b, iv. and v.), what do you anticipate will happen in this market in the long-run?                             
(d)     Determine the long-run equilibrium price and the long-run equilibrium quantity for a single firm in the market. Explain your answer.                 
(e)     Given your answer to question (d), how many units of this good are produced in this market?

Answer 1

A) Perfect competition market Equilibrium at, demand= supply

500-0.5p=-100+p

P*=600/1.5=400

Q=500-0.5*400=500-200=300

B) Individual firm MC=2q+1

Individual firm profit Maximizing quantity is where, market Equilibrium p=MC

P*=MC

400=2q+1

Q=399/2=199.5

ii) profit= TR-TC

TR=199.5*400=79,800

TC=100+199.5*199.5+199.5=40,099.75

Profit=79,800-40,099.75=39,700.25

iii) Because firm is earning positive profit,so it is short run equilibrium.

C)Due to short run super Normal profit, it will attract new firms. So new firms will enter the market in long run and thus Increase market supply and thus lead to decrease in Market price and individual firm profit Decrease to zero.

D)The long run Equilibrium price is Equal to Minimum average cost.

AC= TC/q=100/q +q +1

Average cost is Minimum at where is equal to marginal cost

100/q +q +1=2q+1

100/q=q

Q^2=100

Q=10

P*= min AC= MC=100/10 +10 +1=10+10+1=21

So long run Equilibrium price is 21 and individual firm long run Equilibrium quantity is 10.

E)Given long run equilibrium price=21

Long run Equilibrium quantity will be:

Q=500-0.5*21=500-10.5=489.5