(Solved): Consider a town in which only two residents, Sam and Teresa, own wells that produce water safe for ...

Consider a town in which only two residents, Sam and Teresa, own wells that produce water safe for drinking. Sam and Teresa 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 Sam believes that Teresa is going to collect 12 gallons of water to sell. On the graph, use the purple points (diamond symbols) to plot the demand curve (D1) Sam faces given Teresa's water collection; then use the grey points (star symbol) to plot the marginal revenue curve (MR1) Sam faces. Finally, use the black point (plus symbol) to indicate the profit-maximizing price and quantity (Profit Max 1) in this case. Note: Dashed drop lines will automatically extend to both axes. PRICE (Dollars per gallon) 6.00 5.50 5.00 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0 Market Demand MC 0 2 4 6 8 10 12 14 16 18 QUANTITY (Gallons of water) 20 22 24 ? 0$ MR? + Profit Max 1 Instead, now assume Sam believes that Teresa is going to collect 16 gallons of water to sell, rather than 12. On the following graph, use the purple points (diamond symbol) to plot the demand curve (D2) Sam faces in this case; then use the grey points (star symbol) to plot the marginal revenue curve (MR2) Sam faces. Finally, use the black point (plus symbol) to indicate the profit-maximizing price and quantity (Profit Max 2) in this case. PRICE (Dollars per gallon) 6.00 5.50 5.00 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0 0 Market Demand MC 2 4 6 8 10 12 14 16 18 QUANTITY (Gallons of water) Teresa's Water Production (Gallons of water) 12 16 20 22 24 ? Sam's Water Production (Gallons of water) No MR2 Fill in the following table with the quantity of water Sam produces, given various production choices by Teresa. Profit Max 2 ? Given the information in this table, use the green points (triangle symbol) to plot Sam's best-response function (BRF) on the following graph. Since Sam and Teresa face the same costs for producing water, Teresa's best-response function is simply the reverse of Sam's; that is, the curve has the same shape, but the horizontal and vertical intercept values are switched. Therefore, you can derive Teresa's best-response function by following the same analysis as in the previous question, but from Teresa'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. TERESA'S QUANTITY (Gallons of water) 24 22 20 18 16 14 12 10 0 0 2 O True 4 False 6 8 10 12 14 16 18 20 SAM'S QUANTITY (Gallons of water) 22 24 Sam's BRF Teresa's BRF True or False: According to her best-response function, Teresa will always want to decrease her output as Sam decreases his. Nash Equilibrium