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UCLA
Economics 11 – Fall 2006
Professor Mazzocco
Problem Set 8
Due by November 25 before 7:00pm in the box located outside room 2221E.
1) OPEC can price gasoline as it wishes. Suppose that it knows how demand responds to
changes in prices (p). In particular, it knows that the quantity of barrels of gasoline
demanded (Q) is given by the following function: Q=a*e
(1/5)p
, where “a” is just a
constant.
a) Write an expression for OPEC’s revenues as a function of Q.
First, rewrite the demand function as a function of Q:
p(Q) = 5ln(a) – 5ln(Q)
Revenues are defined as:
R(Q) = p(Q)*Q = (5ln(a) – 5ln(Q))*Q
b) Given that the OPEC only faces a fixed cost, the total cost function is given by:
C(q)=50. Now write an expression for the cartel’s profit function (as a function of Q).
(Q) = R(Q) –C(Q) = (5ln(a) – 5ln(Q))*Q  50
c) Solve the profit maximization problem to find the optimal quantity (Q*) and the
optimal price (p*) the cartel should choose.
MAX
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This note was uploaded on 04/19/2010 for the course ECON Econ 11 taught by Professor Mcdevitt during the Fall '07 term at UCLA.
 Fall '07
 McDevitt
 Economics

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