Suppose Ralph sells bento lunches, which have the following demand:

pR = 100 – qR – 0.5qD
where pR is the price of Ralph's bentos and qR is the number of bentos Ralph sells. qD is the number of bentos Ralph's rival, Dave, sells. Dave's demand is given by:
pR = 100 – qD – 0.5qR
where pD is the price Dave can sell his bentos for. Suppose each seller has a cost per unit (average and marginal) of $1.
a. How does this game differ from the Cournot model with identical products? Why do the demand curves indicate that the goods are differentiated – not perfect substitutes for one another?
b. Compute the best response functions for each seller and the Nash Equilibrium outputs and prices.

a. The output of the rival firm has a smaller effect on the demand for a firm's output than the
firm's own output. This means that customers view the goods as substitutes, but the "own-price effect" is stronger than the substitute's price effect. For example, the market price of coke is more responsive to the quantity of coke supplied than it is to the quantity of Pepsi supplied. In the traditional Cournot model, the goods are perfect substitutes and each firm's output had the same impact on the market prices. Here, it is possible for the goods to have different prices, but in Cournot's model, the goods are sold at the same price.
b. The profit functions are
πR = (100 - qR - 0.5qD)qR - qR
πD = (100 - qD - 0.5qR)qD - qD
The best response functions are
qR = (99 - 0.5qD)/2
qD = (99 - 0.5qR)/2
Solving these simultaneously yields:
qR = qD = 39.6
Each firm sells at the price 40.6.