Evan rides his mountain bike down Whistler each summer weekend. The value he places on each kilometre ridden is given by P=4−0.02Q, where Q is the number of kilometres. He incurs a cost of $2 per kilometre in lift fees and bike depreciation.
(a) How many kilometres will he ride each weekend? [Hint: Think of this “value” equation as demand, and this “cost” equation as a (horizontal) supply.]
(b) But Evan frequently ends up in the local hospital with pulled muscles and broken bones. On average, this cost to the Canadian taxpayer is $0.50 per kilometre ridden. From a societal viewpoint, what is the efficient number of kilometres that Evan should ride each weekend?
a) The number of kilometres Evan will ride each weekend is at the point where,
4 - 0.02Q = 2
0.02Q = 4 - 2 = 2
Q = 2 / 0.02 = 100
Thus, Evan will ride 100 kilometers each weekend.
b) Marginal social cost = 2 + 0.50 = 2.50
The efficient number of kilometres that Evan should ride each weekend is at the point where,
4 - 0.02Q = 2.50
0.02Q = 4 - 2.50 = 1.50
Q = 1.50 / 0.02 = 75
Thus, the efficient number of kilometres that Evan should ride each weekend is 75 kilometers.
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