Question

Suppose that the technology to produce surfboards is according to the cost function C(q) = 4 + 5q + .25q2 where 4 is the sunk fixed cost firms have to incur to enter into this market. Market demand for surfboards is given by: Q = 1550 - 10P. Surfboard producers are price takers, in other words they take the market price as given. a) Find a surfboard producer’s short-run supply curve. (Hint: start with profit maximization of a single firm). b) What is quantity produced by a producer if the market price of a surfboard is P=10TL/surfboard? c) What is the profit of a producer if the market price of a surfboard is P=10TL/surfboard? d) How many firms are there currently in the market if the market price is P=10TL/surfboard? (Hint: Think short-run competitive market equilibrium) e) What do you expect in this market in the long run if there are no barriers to entry or exit into and from this market?

Answer 1

a)

c(q) = 4 + 5q + 0.25q²  

c'(q) = dc/dq = 5 + 0.5q

MC = 5 + 0.5q

Profit maximising condition

P = MC

P = 5 + 0.5q

P - 5 = 0.5q

q = 2P - 10

short run supply curve of surfborad producer is q = 2P - 10

b)

Market price P = 10

q = 2P - 10

q = 2(10) - 10

q = 20 - 10

q = 10

quantity produced by producer is q = 10

c)

Profit   = Pq - C(q)  

= Pq - 4 - 5q - 0.25q²  

= 10(10) - 4 - 5(10) - 0.25(10)²  

= 100 - 4 - 50 - 25

= 100 - 79

= 21

d)

Market demand

Q = 1550 - 10P

Q = 1550 - 10(10)

Q = 1550 - 100

Q = 1450

Market quantity is Q = 1450

Number of firms n = Q/q  

= 1450/10

= 145

e)

since there are no barriers to entry or exit and firms are making a positive profit in short run therefore new firms will enter in the industry or market in the long run.