Problem set #2 answer key. (Note that I have corrected two small typos on
9/22. A spurious reference to an earlier problem 3 in problem 4 was
removed. A reference to part (b) in problem 5 was replaced with a
reference to part (a).)
AEM 4240
Problem Set #2 Answer Key
1. Econ review warmup
a) Hugo has decided to minimize his total costs. How much should he produce? What are
his total profits?
TC increases with Q at all positive values of Q. TC therefore reaches a minimum at the
lowest feasible value of Q, which is 0, at which point profits = 405.
b) Hugo is back in the shop. He understands the importance of amortizing the daily lease
cost of the machine over a large production run. His brotherinlaw, the VP of marketing
firm, has convinced Hugo of the importance of dominating the market and getting as
much
market share as he can with his existing machine. Hugo decides to follow this friendly
advice, believing that not only will he make great heaps of money but he will also achieve
much more pleasant conditions at the next gathering with his inlaws. How much does he
instruct you to produce in order to maximize sales? What are his total profits?
We are given a market price of hugonuts that is not a function of Q.
This implies that no
matter how high Q is, Hugo will be able to sell all of his production at $120.
So to
maximize sales, Hugo simply sets Q as high as possible.
Since Hugo’s capacity is
limited at 100 units by his equipment, he maximizes sales by producing 100 units.
At
this level, profits are 120*100(405+20*100+5*100
2
)= $40,405.
It won’t be a pleasant gathering after all.
c) You notice Hugo has sprouted a few more gray hairs. Coincidentally, the marketing
VP
was called away to investigate a potential new client in Tierra del Fuego. Hugo has
given
the matter more thought, and instructs you to minimize the average cost of production.
How much do you produce? What are your profits?
You have a choice of two methods. At its minimum, you know AC is equal to MC. If the
marginal cost of producing the next unit were below average cost, then AC would still be
falling. If the marginal cost of producing the next unit were above the average cost, then
AC would be increasing. So AC must reach a minimum where AC=MC. AC is found by
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View Full Documentdividing TC by Q, yielding AC=405/Q + 20 + 5Q. MC is found by taking the derivative
of TC with respect to Q, yielding MC=20+10Q. Setting MC=AC and solving for Q you
find that Q=9. Alternatively, AC reaches a minimum where its derivative with respect to
Q is zero:
AC = (405 + 20Q + 5Q
2
)/Q = 405/Q + 20 + 5Q
Take the derivative of this expression:
AC/ Q = 405/Q
∂
∂
2
+ 5
Set it equal to zero and solve for Q:
405/Q
2
+ 5 = 0
405/Q
2
= 5
81 = Q
2
Q = 9
So average cost is minimized at Q=9. Profits are 120*940520*95* 9
2
=$90.
d) Hugo is looking a bit better. He almost smiles now, especially when he shows
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 Fall '07
 BLALOCK,G.
 Economics, Microeconomics, Alfalfa Room

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