For an office building in a large city, the profit increases with the number of floors for the first 40 floors at a rate of $3 million per floor, and then decreases as the number of floors increases at a rate of $2 million per floor. In addition, the prize or bonus profit from the tallest building is $30. Two firms, A and B, will each build one office building. In the event of a tie (two buildings of the same height) there is no prize, meaning that there will not be two tallest building at the same time because both firms are better off with just one winner.

a)Draw a graph for the profit for the firms with respect to different number of floors, i.e. draw the profit on the y-axis and the number of floors on the x-axis. (6 points)

b)State the equilibrium number of floors for the tallest building, identify that point on your graph in part (a). (6 points)

c)State the equilibrium number of floors for the second tallest building, identify that point on your graph in part (a). (6 points)

Question

For an office building in a large city, the profit increases with the number of floors for the first 40 floors at a rate of $3 million per floor, and then decreases as the number of floors increases at a rate of $2 million per floor. In addition, the prize or bonus profit from the tallest building is $30. Two firms, A and B, will each build one office building. In the event of a tie (two buildings of the same height) there is no prize, meaning that there will not be two tallest building at the same time because both firms are better off with just one winner.

a)Draw a graph for the profit for the firms with respect to different number of floors, i.e. draw the profit on the y-axis and the number of floors on the x-axis. (6 points)

b)State the equilibrium number of floors for the tallest building, identify that point on your graph in part (a). (6 points)

c)State the equilibrium number of floors for the second tallest building, identify that point on your graph in part (a). (6 points)

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For an office building in a large city, the profit increases with the number of floors for the first 40 floors at a rate of

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