Principles of Microeconomic Theory 1: Problem Set 3

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Principles of Microeconomic Theory 1: problem set 3.

Part A：Multiple choice questions.

Question 1. suppose that a consumer,s preferences are represented by the utility function U = “q1 “q2. There are three bundles of goods available:

a = (64, 4)

b = (16, 16)

c = (16, 4)

which one of the following statements is false?

(a)  The consumer has revealed that a 之 b.

(b) The consumer has revealed that a ~ b.

(c) Because U(b) = 2U(c), we know that the consumer prefers b to c.

(d) Because U(b) = 2U(c), we know that the consumer likes b twice as much as c.

(e) If all of these bundles were afordable, the consumer would not choose c.

Question 2. suppose that a consumer has utility function U(q1 , q2 ) = q1(4) q2(3) . which one of

the following statements is correct?

(a) If q1  = q2 , then the slope of the consumer,sindiference curve at (q1 , q2 ) is -  . (b) If q1  = q2 , then the slope of the consumer,sindiference curve at (q1 , q2 ) is -  . (c) If q1  = q2 , then the slope of the consumer,sindiference curve at (q1 , q2 ) is -  . (d) If q1  = q2 , then the slope of the consumer,sindiference curve at (q1 , q2 ) is -6.

(e) None of the above.

Question 3. suppose that the consumer,s preferences are represented by:

U(q1 , q2 ) = min {2q1 , q2 } .

The consumer faces prices p1  = 10 and p2  = 10 and has income Y  = f1000.  The con- sumer,s optimal bundle is given by which one of the following?

(a)（q 1(*), q2(*))= (50, 50).

(b)（q 1(*), q2(*))= (100, 0).

(c)（q 1(*), q2(*))= (0, 100).

(d)（q 1(*), q2(*) , ).

(e)（q 1(*), q2(*) , ).

Part B：written answer questions.

Question 4. A consumer has preferences represented by the utility function:

U(q1 , q2 ) =  ln q1 +  ln q2 .

The consumer has income Y = f3000 and faces prices p1  = f20 and p2  = f30.

Formulate the consumer,s problem as a constrained optimisation and solve using the La-  grangian approach. You may assume that an interior solution exists (that is, positive amounts of both goods are consumed at the optimum). produce a diagram.

Question 5. Reading the sunday supplement, you come across the following commentary:

“The theory of consumer choice in economics is complete nonsense.  con- sumers do not have utility functions in their heads, they do not formulate La- grangians, nor do they solve systemsofirst order conditions. Most have never even heard of constrained optimisation theory.  consumers just choose what they like best out of what they aford. Economics must be overthrown!”

Discuss!


2023-08-25