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Janet's Water Production (Gallons of water) 8 12 Felix's Water Production (Gallons of water) Given the information in this table, use the green points (triangle symbol) to plot Felix's best-response function (BRF) on the following graph. Since Felix and Janet face the same costs for producing water, Janet's best-response function is simply the reverse of Felix's; that is, the curve has the same shape, but the horizontal and vertical intercept values are switched. Therefore, you can derive Janet's best-response function by following the same analysis as in the previous question, but from Janet'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.

Janet's Water Production (Gallons of water) 8 12 Felix's Water Production (Gallons of water) Given the information in this table, use the green points (triangle symbol) to plot Felix's best-response function (BRF) on the following graph. Since Felix and Janet face the same costs for producing water, Janet's best-response function is simply the reverse of Felix's; that is, the curve has the same shape, but the horizontal and vertical intercept values are switched. Therefore, you can derive Janet's best-response function by following the same analysis as in the previous question, but from Janet'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.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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2. Cournot competition Consider a town in which only two residents, Felix and Janet, own wells that produce water safe for drinking. Felix and Janet 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 Felix believes that Janet is going to collect 8 gallons of water to sell. On the graph, use the purple points (diamond symbols) to plot the demand curve (D₁) Felix faces given Janet's water collection; then use the grey points (star symbol) to plot the marginal revenue curve (MR₁) Felix 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 PRICE (Dollars per gallon) 5.00 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0 6.00 5.50 JANET'S QUANTITY (Gallons of water) 5.00 4.50 4.00 3.50 Instead, now assume Felix believes that Janet is going to collect 12 gallons of water to sell, rather than 8. 3.00 On the following graph, use the purple points (diamond symbol) to plot the demand curve (D2) Felix faces in this case; then use the grey points (star symbol) to plot the marginal revenue curve (MR2) Felix faces. Finally, use the black point (plus symbol) to indicate the profit-maximizing price and quantity (Profit Max 2) in this case. 2.50 2.00 1.50 1.00 0.50 0 24 22 20 18 16 14 12 10 Market Demand Janet's Water Production Felix's Water Production (Gallons of water) (Gallons of water) 8 12 8 MC 6 0 2 4 2 0 4 MC Market Demand 0 2 Fill in the following table with the quantity of water Felix produces, given various production choices by Janet. 6 8 10 12 14 16 18 QUANTITY (Gallons of water) Given the information in this table, use the green points (triangle symbol) to plot Felix's best-response function (BRF) on the following graph. Since Felix and Janet face the same costs for producing water, Janet's best-response function is simply the reverse of Felix's; that is, the curve has the same shape, but the horizontal and vertical intercept values are switched. Therefore, you can derive Janet's best-response function by following the same analysis as in the previous question, but from Janet'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. ? 20 22 24 4 0 2 6 8 10 12 14 16 18 20 22 24 QUANTITY (Gallons of water) D₁ MR1 + Profit Max 1 4 6 8 10 12 14 16 18 20 22 24 FELIX'S QUANTITY (Gallons of water) D₂ MR2 + (?) Profit Max 2 Felix's BRF (?) Janet's BRF + Nash Equilibrium
Transcribed Image Text:2. Cournot competition Consider a town in which only two residents, Felix and Janet, own wells that produce water safe for drinking. Felix and Janet 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 Felix believes that Janet is going to collect 8 gallons of water to sell. On the graph, use the purple points (diamond symbols) to plot the demand curve (D₁) Felix faces given Janet's water collection; then use the grey points (star symbol) to plot the marginal revenue curve (MR₁) Felix 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 PRICE (Dollars per gallon) 5.00 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0 6.00 5.50 JANET'S QUANTITY (Gallons of water) 5.00 4.50 4.00 3.50 Instead, now assume Felix believes that Janet is going to collect 12 gallons of water to sell, rather than 8. 3.00 On the following graph, use the purple points (diamond symbol) to plot the demand curve (D2) Felix faces in this case; then use the grey points (star symbol) to plot the marginal revenue curve (MR2) Felix faces. Finally, use the black point (plus symbol) to indicate the profit-maximizing price and quantity (Profit Max 2) in this case. 2.50 2.00 1.50 1.00 0.50 0 24 22 20 18 16 14 12 10 Market Demand Janet's Water Production Felix's Water Production (Gallons of water) (Gallons of water) 8 12 8 MC 6 0 2 4 2 0 4 MC Market Demand 0 2 Fill in the following table with the quantity of water Felix produces, given various production choices by Janet. 6 8 10 12 14 16 18 QUANTITY (Gallons of water) Given the information in this table, use the green points (triangle symbol) to plot Felix's best-response function (BRF) on the following graph. Since Felix and Janet face the same costs for producing water, Janet's best-response function is simply the reverse of Felix's; that is, the curve has the same shape, but the horizontal and vertical intercept values are switched. Therefore, you can derive Janet's best-response function by following the same analysis as in the previous question, but from Janet'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. ? 20 22 24 4 0 2 6 8 10 12 14 16 18 20 22 24 QUANTITY (Gallons of water) D₁ MR1 + Profit Max 1 4 6 8 10 12 14 16 18 20 22 24 FELIX'S QUANTITY (Gallons of water) D₂ MR2 + (?) Profit Max 2 Felix's BRF (?) Janet's BRF + Nash Equilibrium
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