2. Cournot competition Consider a town in which only two residents, Edison and Hilary, own wells that produce water safe for drinking. Edison and Hilary can pump and sell as much water as they want at no cost. Assume that outside water cannot be transported into the town for sale. The following questions will walk you through how to compute the Cournot quantity competition outcome for these duopolists. Consider the market demand curve for water and the marginal cost for collecting water on the following graph. Assume Edison believes that Hilary is going to collect 8 gallons of water to sell. 0n the graph, use the purple points (diamond symbols) to plot the demand curve (D1) Edison faces given Hilary's water collection; then use the grey points (star symbol) to plot the marginal revenue curve (MR1) Edison faces. Finally, use the black paint (plus symbol) to indicate the prot- maximizing price and quantity (Prot Max 1) in this case. Note: Dashed drop lines will automatically extend to both axes. 12 Market Demand 11 o 10 D1 9 'E' ]$| 2 8 E a: 7 MR1 Q. In E 6 "l' E . e 5 Lu Prot Max1 Q 4 DC a. 0 4 812162024283236404448 QUANTITY (Gallons of water) Instead, now assume Edison believes that Hilary is going to collect 16 gallons of water to sell, rather than 8. On the following graph, use the purple points (diamond symbol) to plot the demand curve (D2) Edison faces in this case; then use the grey points (star symbol) to plot the marginal revenue curve (MR2) Edison faces. Finally, use the black point (plus symbol) to indicate the profit-maximizing price and quantity (Profit Max 2) in this case. 12 Market Demand 11 10 D 2 MR 2 PRICE (Dollars per gallon) .+ Profit Max 2 w N MC 0 4 8 12 16 20 24 28 32 36 40 44 48 QUANTITY (Gallons of water)Fill in the following table with the quantity of water Edison produces, given various production choices by Hilary. Hilary's Water Production Edison's Water Production (Gallons of water) (Gallons of water) 8 16 Given the information in this table, use the green points (triangle symbol) to plot Edison's best-response function (BRF) on the following graph. Since Edison and Hilary face the same costs for producing water, Hilary's best-response function is simply the reverse of Edison's; that is, the curve has the same shape, but the horizontal and vertical intercept values are switched. Therefore, you can derive Hilary's best-response function by following the same analysis as in the previous question, but from Hilary's perspective. Use the purple points (diamond symbol) to plot her best-response function on the graph. Finally, use the black point (plus symbol) to indicate the unique Nash equilibrium under Cournot quantity competition. 48 44 A 40 Edison's BRF Hilary's BRF HILARY'S QUANTITY (Gallons of water) Nash Equilibrium A 4 12 16 20 24 28 32 36 40 44 48 EDISON'S QUANTITY (Gallons of water)True or False: According to her best-response function, Hilary will always want to increase her output as Edison decreases his. O True O False