Three (3) identical rms produce widgets. Each rm faces a constant marginal cost of $10 per widget, and has xed costs of $15,000. The rms compete by selecting quantities (Cournot Competition). Inverse demand in the market is given by the equation,

P = 50(Q/100)

where P represents the market price and Q is the total quantity produced by the three rms.

Required:

(a) Derive the total cost function for the typical rm. (Hint: Use QA to represent the quantity produced by this rm.)

(2 marks)

(b) Derive the prot function for the typical rm. (Hint: Use X to represent the combined production of the remaining two rms.)

(3 marks)

(c) Derive the best response function for the typical rm.

(3 marks)

(d) Find the equilibrium quantity of the typical rm.

(2 marks)

(e) Find the equilibrium market price and the prots of the typical rm.

(3 marks)

(f) Explain how would you expect the structure of this market to change over time. Maximum length 100 words. (Hint: You do not need to do any further calculations for this part of the question.)

(2 marks)