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Economics

ECO380H1

Carlos Serrano

Fall

Description

UNIVERSITY OF TORONTO
Faculty of Arts and Science
October 2010 MIDTERM EXAMINATION PRACTICE QUESTIONS
ECO380F
Non-programmable calculators are allowed
No other aids allowed
Question 1 [Product diﬀerentiation] (40 points)
Consider the "Not so easy" Hotelling model we discussed in the lecture. That is where transportation
costs are quadratic and there is a marginal cost 0 of production. To study location (product) compe-
tition, we considered a two period game. In the ﬁrst period ﬁrms chose location simultaneously. In the
second period ﬁrms chose prices simultaneously.
To solve the model, we started solving it from its second period. You proved in the homework that
proved that the demand function ofﬁrm1and2were () and (). Immediately after, you solved
1 2
that the second period equilibrium prices were 1() and 2() whichdependonthelocationof ﬁrm 1
and2. ethensolvedthe ﬁrst period problem of the ﬁrms. You also showed that when the ﬁrms chose
location there was a trade-oﬀ between moving to the center or to the extremes. In this question, I want to
focus on this trade-oﬀ.
(a) Explain what this trade-oﬀ is about. Please, be speciﬁc and use the technical terms (including the
sign of the derivatives) that appeared in the homework whenever possible. These technical terms (including
sign of the derivatives) were the results that you were supposed to prove. Note: here you don’t have to
proveanything,youjusthavedescribeandusetheseresultsinyouranswer.(25points)
(b) Did the ﬁrms ﬁnd it optimal to move to either the center, locate at the extremes or stay somewhere
in between? Explain. (10 points)
Question 2: [Price discrimination] (20 points) 1
Consider the maximization problem of a telephone company, Telefonica S.A. Assume that Telefonica,
a monopolist, has ﬁxed costs 0 of operation and a cost =10 per unit supplied of telephone services.
There are two type of customers: There are 2 type-1 customers with individual (inverse) demand
(1)=50 − 1
and there are 5 type-2 customers with individual (inverse) demand
(2)=50 − 10 2
where s the quantity demanded by customer type- and is the price per unit of telephone services.
Suppose that each customer pays a connect ﬁxed fee charge to use the telephone system and a usage
price per unit of telephone services. Assume that the telephone company must charge to all customers the
same ﬁxed fee and same usage price per unit of telephone services. Assume that the telephone company is
serving both type of customers.
Consider that the telephone company hires you as an economic advisor. The telephone company wants
to maximize proﬁts under the conditions speciﬁed above. Suppose that the ﬁxed cost are suﬃciently low
that the ﬁrm will operate.
(a) Calculate what is the optimal ﬁxed fee charged, , as a function of the price per unit of telephone
services ?7o)t
(b) Write the maximization problem that the telephone company solves to maximize proﬁts? Please,
write the proﬁt function as a function of . You don’t have to calculate the speﬁcic (7 points)
(c) After making your proposal to management, a MBA graduate suggests that proﬁts are maximized
when marginal revenue equals marginal cost, and consequently Telefonica should charge the monopoly
price and set =0 ( is the uniform monopoly price). Explain in simple terms, as if you had to
convince the management team, whether or not the MBA graduate is correct. It is not necessary to make
calculations. (6 points)
1
According to my ﬁnal exam policy, an answer-key to this question will not be available.
1 Question 3: [Third Degree Price Discrimination]
Suppose there are two kinds of consumers, and . The inverse demand curves for the two markets
are =16 − an =20 − The seller in the market is a monopolist with cost function ()=2 .
(a) Suppose the ﬁrm can discriminate between the two markets and practice third degree price discrim-
ination. Suppose in market ∈ {},the ﬁrm oﬀers a uniform price . Sol

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