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ECN100A (INTERMEDIATE MICROECONOMICS)
PROBLEM SET 3
DUE BEGINNING OF CLASS: FRIDAY, MARCH 15, 2019
Question 1: After a cruise ship accident, Annie and Bert are deserted on an island. All that Annie
managed to save was 4 bags of chips (C) and 4 bottles of Dr. Pepper (D). Bert, however, managed
to save 6 bags of chips but no bottles of Dr. Pepper.
(a) Draw a properly labeled Edgeworth Box and indicate Annie and Bert’s “endowments”.
(b) Suppose you find some binoculars and observe Annie trade Bert 1 bottle of Dr. Pepper
for 1 bag of chips (i.e. barter trade) after which there is no longer any trading. Draw an
indifference curve for each of Annie and Bert that is consistent with this trade.
(c) Suppose out of boredom, Annie and Bert had instead created their own currency to buy
and sell chips and Dr. Pepper with each other through the market (i.e. items for cash)
and that current prices are pC = p D = 1. In a new Edgeworth Box, indicate the original
allocation and the new allocation after the previous barter trade. Indicate the set of bundles
that are affordable for Annie and Bert. [Hint: Imagine if Annie sold all of her items at
market prices; how much cash would she get for them, and then what could she afford to
buy with that cash?].
(d) Using this market mechanism, you observe the Annie and Bert each consuming the same
bundle as they did under barter trading. Draw indifference curves consistent with this
A , MRS B , and
trade on your diagram from (c). What is the relationship between MRSCD
CD
pC
at
the
point
representing
their
final
consumption
bundles?
pD
Question 2: After the same cruise ship accident, Ron and Don are deserted on a separate island.
Unfortunately for them, they did not manage to bring anything with them. On the island, there
are only two edible items: Bananas (B) and Coconuts (C). Each day, Ron and Don go and collect
fruit. Ron is twice as good at collecting bananas as he is at collecting coconuts and the maximum
number of bananas he could collect in a day is 24. Don is the opposite: he is twice as good at
collecting coconuts as he is at collecting Bananas and could collect a maximum of 24 coconuts in a
day.
(a) Suppose Ron and Don are not getting along (Don accused Ron of stealing his binoculars)
and refuse to trade. Draw a diagram showing the production possibilities frontier for Don,
and a separate diagram for Ron.
(b) For Ron, what is the “price” of collecting a coconut? What about for Don?
(c) Suppose Ron and Don both have the same utility function: U = B0.5 C0.5 . How many
bananas and coconuts will Ron and Don each produce (and then consume)?
1
(d) After some time, Ron and Don reconcile and discuss the possibility of trading with one
another. By cooperating, how much of each fruit will Ron and Don produce? Will they be
better off?
(e) Suppose they play the same market game as Annie and Bert to escape boredom, and the
prices are p B = p D = 1. How much fruit will each person collect? At these prices, how
many bananas are demanded by Don and how many bananas is Ron willing to supply?
Question 3: Comcast has a monopoly in Davis for anyone who likes very high speed broadband.
Demand for Comcast’s broadband internet in Davis is q( p) = 250 − p where p is the monthly
price of broadband and q is the number of households who will subscribe to their broadband at
that price. Comcast’s costs are largely the infrastructure costs of laying coaxial cable in the ground;
once installed, the operating costs are low. Let Comcast’s cost function be C (q) = 10q + 4000.
(a) What is Comcast’s profit function?
(b) Re-write Comcast’s profit function in terms of the quantity of households Comcast intends
to have subscribe and then take the derivative of that with respect to q and set it equal to
zero.
(c) Which terms correspond to Comcast’s marginal revenue, MR(q), and which to its marginal
costs, MC (q)?
(d) Solve for Comcast’s optimal quantity and price of broadband in Davis.
(e) Why did Comcast’s fixed costs play no role in determining the price?
(f) Draw a diagram showing Comcast’s inverse demand curve (i.e. price on the vertical axis,
quantity on the horizontal axis) and plot the profit maximizing price and quantity chosen
by Comcast. Which areas correspond to consumer surplus, Comcast’s variable profit, and
the deadweight loss arising from monopoly?
2

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