Alex and Becky each rent one unit of a two-unit apartment building. The building has two separate furnaces located between the two apartments. The renters each control and pay for the heat their furnaces generate and would choose to increase the temperature of their apartments by 30 degrees if the other never turned on their furnace, given that the marginal private benefit (MB) of the 30th degree is equal to the marginal cost (MC) of 1 degree of heat (assume that the MC of heat is constant and that the MB of heat is decreasing). However, each degree of heat paid for by one not only raises the temperature in that apartment by a degree but also raises the temperature in the other apartment by half a degree. As a result, if Becky were to buy 10 degrees of heat, then Alex would need to purchase only[ marginal benefit of the final degree was equal to the marginal cost. degrees of heat before his personal

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Chapter1: Making Economics Decisions
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Alex and Becky each rent one unit of a two-unit apartment building. The building has two separate furnaces located between the two apartments. The
renters each control and pay for the heat their furnaces generate and would choose to increase the temperature of their apartments by 30 degrees if
the other never turned on their furnace, given that the marginal private benefit (MB) of the 30th degree is equal to the marginal cost (MC) of 1 degree
of heat (assume that the MC of heat is constant and that the MB of heat is decreasing). However, each degree of heat paid for by one not only raises
the temperature in that apartment by a degree but also raises the temperature in the other apartment by half a degree.
As a result, if Becky were to buy 10 degrees of heat, then Alex would need to purchase only
marginal benefit of the final degree was equal to the marginal cost.
Use the blue line (circle symbol) to plot Alex's best-response function (BRF) on the following graph, with the total amount of heat he will buy on the
vertical axis as a function of the total amount Becky buys (horizontal axis). (Hint: Alex's response to Becky's purchase noted previously represents
one point on the line, and the response when Becky purchases 0 degrees of heat will be the vertical intercept.) Then, use the orange line (square
symbol) to plot Becky's best-response function, with the total amount she will buy (horizontal axis) as a function of the total amount Alex buys
(vertical axis). Finally, place the black point (plus symbol) on the graph to indicate the Nash equilibrium amount of heat each person will purchase,
given the other's equilibrium choice.
Note: Dashed drop lines will automatically extend to both axes.
HEAT BOUGHT BY ALEX
90
80
2 8 8 9
8
20
10
D
0
10
30 40 50
70
HEAT BOUGHT BY BECKY
True
80 90 100
O False
Alex's BRF
Becky's BRF
+-
Nash Equilibrium
Suppose the government is worried about the low temperatures and wants to increase heat consumption.
?
degrees of heat before his personal
True or False: The current Nash equilibrium is inefficiently high; therefore, the government should implement a tax on heat to reach its goal.
Transcribed Image Text:Alex and Becky each rent one unit of a two-unit apartment building. The building has two separate furnaces located between the two apartments. The renters each control and pay for the heat their furnaces generate and would choose to increase the temperature of their apartments by 30 degrees if the other never turned on their furnace, given that the marginal private benefit (MB) of the 30th degree is equal to the marginal cost (MC) of 1 degree of heat (assume that the MC of heat is constant and that the MB of heat is decreasing). However, each degree of heat paid for by one not only raises the temperature in that apartment by a degree but also raises the temperature in the other apartment by half a degree. As a result, if Becky were to buy 10 degrees of heat, then Alex would need to purchase only marginal benefit of the final degree was equal to the marginal cost. Use the blue line (circle symbol) to plot Alex's best-response function (BRF) on the following graph, with the total amount of heat he will buy on the vertical axis as a function of the total amount Becky buys (horizontal axis). (Hint: Alex's response to Becky's purchase noted previously represents one point on the line, and the response when Becky purchases 0 degrees of heat will be the vertical intercept.) Then, use the orange line (square symbol) to plot Becky's best-response function, with the total amount she will buy (horizontal axis) as a function of the total amount Alex buys (vertical axis). Finally, place the black point (plus symbol) on the graph to indicate the Nash equilibrium amount of heat each person will purchase, given the other's equilibrium choice. Note: Dashed drop lines will automatically extend to both axes. HEAT BOUGHT BY ALEX 90 80 2 8 8 9 8 20 10 D 0 10 30 40 50 70 HEAT BOUGHT BY BECKY True 80 90 100 O False Alex's BRF Becky's BRF +- Nash Equilibrium Suppose the government is worried about the low temperatures and wants to increase heat consumption. ? degrees of heat before his personal True or False: The current Nash equilibrium is inefficiently high; therefore, the government should implement a tax on heat to reach its goal.
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