Question 1 (60 points)
An auto shop specializing in brake repair faces the following weekly costs: rent, $500; labor, $400 per
worker; parts and supplies, $30 per repair. Each worker can repair three cars per week.
– For each column, give the appropriate equation used to calculate the variable in question.
– Fill in the spaces in the table below.
– When are TC and FC equal?
Car Repairs Workers Total cost Fixed cost Variable cost Average
total cost
Marginal
cost
0
3
6
9
12
15
Question 2 (30 points)
If there are 10 identical firms in a competitive market where supply and demand are given by the following
equations:
???????? = 5????
???????? = 100 ? 4????
– Find the market price and quantity.
Those companies are merged and the government issues a law that grants it a monopoly. The merger
doesn’t change the ability to produce, thus the marginal cost curve of the new firm coincides with the
supply curve of the old market, and it’s given by the following equation:
???????? = 0.2????
If demand doesn’t change, marginal revenue is given by the following equation:
???????? = 25 ? 0.5????
– How much will the company produce? How much will it charge?
– Compare your results obtained under competition and under monopoly. In which case is quantity
higher? In which case is price higher? Why does that happen?
Question 3 (10 points)
Why does the marginal cost curve intersect the average cost curve at its minimum?
Question 4
Bonus question (if you get it right, you will get 5 additional points; if you get it wrong or don’t answer, you
can still get 100 if all other answers are correct). Note that the maximum grade of this homework is 100
regardless of how many points you score.
Only for those who know calculus.
Prove that, for a linear demand curve, the MR curve has the same intercept as the demand curve, but it’s
twice as steep. You can use a generic demand curve of the form:
???? = ???? ? ????????????
Where ???? and ???? are random parameters, ???? is price and ???????? is the quantity demanded.
Hint: remember that marginal implies taking a derivative.
ScholarMatic: Explanation & Answer
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