Assume that an industry with two rms faces an inverse market demand of P = 100 Q. The product is homogeneous, and each rm has a cost function of 600 + 10q + 0.25q².

Assume rms agree to equally share the market.

a. Derive each rm's demand curve.

b. Find each rm's preferred price when it faces the demand curve in derived in part a.

c. Now assume that rm 1's cost function is instead 25q + 0.5q 2 while rm 2's is as before. (This assumption applies to the remaining parts.) Find each rm's preferred price when it faces the demand curve derived in part a.

d. Compute each rm's prot when rm 1's preferred price is chosen. Do the same for rm 2's preferred price. Which price do you think rms would be more likely to agree on? Why?

e. Show that neither price maximizes joint prots.

f. Find the price that maximizes joint prots. Hint: It is where marginal revenue equals both rms' marginal cost.

g. Would rm 1 nd the solution in part f attractive? If not, would a side payment from rm 2 to rm 1 of $500 make it attractive?

Please answer parts E, F & G