ECON 2020:B Intermediate Microeconomics I: Production

ECON 2020:B
Intermediate Microeconomics I: Production
Problem Set # 2
Maya Papineau
Department of Economics, Carleton University
Fall 2015
Due Date: September 29, 2015
In this problem set, as in all following ones and the exams, the term marginal refers to an
infinitesimally small increment. In other words, use derivatives to determine marginal products etc.
You can keep your answers brief, but you should still show the necessary steps. Make sure to
explain your answers in a few words as well.

1

Opportunity and sunk costs (4 points)

(a) What is the opportunity cost of an extra 10h shift at work, if your alternatives are to spend a
maximum of 4h with friends at a bar (valued at 30$/h), doing problem sets for a maximum of
2h (valued at 10$/h), and surfing for any amount of time (valued at 15$/h) [You can combine
activities as you wish.]? (2)
(b) You have just purchased a house for $400,000, paid $24,000 for legal fees and $17,000 for
renovations. The market price of the house does not change. If the sales tax on a house were
3% (to be paid by you if you sell the house), what is the sunk cost of this purchase? (2)

2

Short-run costs (6 points)

A film studio in Hollywood produces movies according to the function (yes, they can also produce
fractions of movies... Think of half a movie as a B-movie or so.)
q = F (K, L) = (2/100)K 0.5 L0.5 .
In the short run, capital (studios, gear) is fixed at a level of 100. It costs $40 (in thousands) to
rent a unit of capital and $10 (in thousands) to hire a unit of labor (actors, stuntmen, camera crew
etc.).
(a) What is the fixed cost? What is the variable cost as a function of output q?1 (2)
1 Hint: You know what K is. From the production function, you can now determine what L has to be as a function
of output q. Once you know what L(q) is, it should be easy to find variable cost.

1

(b) What is the marginal cost (MC) and the average cost (AC) of a movie? What is the average
variable cost and average fixed cost? (2)
(c) Where do the average and marginal cost curves intersect? What is the derivative of the AC
curve and what value does it take at the intersection? What does it tell you about minimum
average cost? (2)

3

Long-run costs (8 points, 2 Bonus Points)

The same Hollywood studio is doing its planning for the next year and can choose capital and labor.
(a) What is the isocost line for a budget of $16 million? What is the equation for the isoquant?
Find the slope (the derivative) of this isoquant and this isocost line.2 What condition has to
hold so that you minimize costs? The minimized cost as a function of output q is C(q) =
2000q (where Cost is in thousands of $), so how many movies can you afford to produce at the
afore-mentioned budget? (4)
(b) What is the additional cost of an additional movie now? How much does it cost on average to
produce a movie? (2)
(c) Comparing these costs to the situation when you have 100 units of capital as in question 2, then
is your average cost higher or lower [assuming you want to produce 8 movies]? What about the
marginal cost? Briefly state why. (2)
(d) Bonus Question: Imagine that you come in as a new manager and discover that the current
capital-labor ratio is K/L = 1. If you spend 100 additional (marginal) dollars on hiring more
labor, how many additional (marginal) units of labor can you hire and how much more output
can you produce? Answer the same for capital. If you have to stay on the same budget, would
you hire or fire workers? (2)

4

Multiple-choice question (2 points)

With economies of scope,
(a) costs are lower when producing more;
(b) it is less expensive to produce goods jointly than separately;
(c) the production possibility frontier is a straight line;
(d) it is less expensive to specialize production on one product.

2 Hint: Remember that both isoquant and isocost tell you what K is as a function of L (and depending on q and
C respectively).

2