3.A third brother, Rex Carr, owns a junkyard. Rex can use one of two methods to wreck cars. The first involves using a hydraulic crusher that costs $200 per year to own, and then spending $1 to dispose of the remains of each crushed car. The second involves buying a shovel each year for $10(the shovels last only a year), and paying his brother Scoop $5 for each car he buries.
a.Write down total cost functions for each of the two technologies(crusher versus Scoop).Write down the average and marginal cost functions for each of the two technologies.
b.If Rex wrecks 40 cars per year, which method should he use? If Rex wrecks 50 cars per year, which method should he use? What is the smallest number of cars for which it would pay him to buy a hydraulic smasher?
A. For the two methods, where Q is output per year, a) the total cost functions is :
TC1= 200 + Q,
and TC2= 10 + 5Q.
(b) The first method has an average cost function
AC1= TC1 / Q= 200 / Q+1
and a marginal cost function
MC1= TC1 Q= 1.
These expenses are AC2= 10 / Q+ 5
and MC2= 5 for the second method.
B. (1) - If Rex wrecks 40 cars per year he should use method 2
(2) If Rex wrecks 50 cars per year he should use method 1
(3) 48 cars per year is the smallest number of cars for which it would pay him to buy a hydraulic smasher.
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