Question

(a)The inverse market demand in a homogeneous-product Cournot duopoly is:

= 10 (₁ + ₂)

and the costs are zero.

(i)Find the marginal revenue for the two firms.

(ii)Determine the reaction for each firm.

(iii)Calculate each firm's equilibrium output.

(iv)Calculate the equilibrium market price.

(v)Calculate the profit of each firm earns in equilibrium.

(b)The global financial crisis and the collapse of the real estate market bubble have created substantial uncertainty for real estate developers. Suppose you are the only builder in a particular residential area, and you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 75 percent chance of low demand and a 25 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are:

P = 125,000 - 150Q and P = 400,000 - 182Q, respectively. Your cost function is C(Q) = 155,000 + 125,250Q.

Required:

(i)How many new homes should you build?

What profits can you expect?