Suppose that in a particular market, the inverse demanded for hasenpfeffer is given by P = 100 - Q. The market is served by two Cournot competitors, Hansel and Gretel, whose quantities are denoted qH and qG, respectively. Both competitors can produce hasenpfeffer at a constant marginal and average total cost of $10.
a. Find the Cournot equilibrium output and price.
b. Suppose that demand doubles so that at each price, twice as many servings are demanded as before.
Specifically, P = 100 - 0.5Q. What happens to the Cournot price and quantity as a result of the increase in demand?
c. Suppose that the original demand doubles, but in a different way, so that each customer is willing to pay twice as much as before to obtain hasenpfeffer. Specifically, P = 200 - 2Q. What happens to the Cournot price and quantity as a result of the increase in demand?
d. Would your answers to (b) and (c) remain the same if Hansel and Gretel were Bertrand competitors rather than Cournot competitors?