Midterm Exam 1 (Group C): ECON 100A
Monday, 10/26/2020
Instructions. You have 65 minutes to solve these questions. To get full credits you need to provide a
detailed justi…cation of your claims. Please write Group C in your answer.
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1. Marcos has preferences represented by utility function U (x1 ; x2 ) = (x1 ) (x2 ) : The consumer has
an income level of m = 2; 000 dollars. The price of good 1 is p1 = 5 and the price of good 2 is p2 = 5.
(a) Compute the Marginal Utility of good 2. (10 Points)
(b) Compute the Marginal Rate of Substitution (in absolute value). (10 Points)
(c) Find the optimal levels of consumption for Marcos (x1 and x2 ). (10 Points)
(d) Suppose the government does not allow Marcos to consume more than 50 units of good 1. Find
the optimal level of consumption of good 2 for Marcos. (10 Points)
2. Martha has preferences represented by utility function U (x1 ; x2 ) = 4x1 + 3x2 : The consumer has an
income level of m = 2; 100 dollars. The price of good 1 is p1 = 3 and the price of good 2 is p2 = 1.
(a) Find a bundle (x1 ; x2 ) that belongs to the same indi¤erence curve of bundle (x1 = 4; x2 = 1) :
(10Points)
(b) Compute the Marginal Rate of Substitution (in absolute value) and …nd the optimal levels of
consumption for Martha (x1 and x2 ). (10 Points)
(c) Suppose the government imposes a per-unit sales tax of $2 on good 2. Find the optimal levels
of consumption for Martha (x1 and x2 ). (10 Points)
3. A consumer buys only two goods, x1 and x2 . Initially, the prices are (p1 ; p2 ) = (1; 3) and the
consumer chooses (x1 ; x2 ) = (3; 3). Later, the prices change to (p1 ; p2 ) = (3; 1). At these new prices
the consumer chooses (x1 ; x2 ) = (2; 5):
(a) Compute the income of the consumer at the two price vectors. (10 Points)
(b) Are these choices consistent with utility maximization? (10 Points)
(c) Can you state whether the consumer prefers bundle (x1 ; x2 ) = (3; 3) or bundle (x1 ; x2 ) = (2; 5)?
(10 Points)
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