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Principles of Microeconomic Theory 1: problem set 4.

Question 2. Assuming rational, monotonic preferences over bundles of two goods (1 and 2) and diminishing marginal rates of substitution, which one of the following statements is false?

(a) Normal goods must obey the law of demand.

(b) If a good violates the law of demand, that good must be inferior.

(c) only inferior goods can violate the law of demand.

(d) Inferior goods must violate the law of demand.

(e) Normal goods cannot violate the law of demand.

Question 3. A consumer has rational, monotonic preferences over bundles of two goods (1 and 2). His indiference curves exhibit diminishing marginal rates of substitution. The price of good 1 decreases, and the consumer,s demand for that good does not change. which one of the following statements is correct?

(a) Good 1 cannot be an inferior good.

(b)  Good 1 must be a normal good.

(c) Good 1 must be an inferior good.

(d) Good 1 must be a luxury good.

(e) The Engel curve associated with good 1 is everywhere increasing.

part B: written answer question.

Question 4.  A consumer has preferences represented by the utility function U(q1 , q2 ) = ( ℼq1 + “q2 )2 .  The consumer has income Y  = f5000 and p2   = f40.  Derive the con- sumer,s demand function for good 1 as afunction of p1 .