Problem sheet question prompts

Question 1

What does it mean if a consumer has a linear utility function? Which 2 ways could one solve for demand function? How would the solution look? (Q1, PS1)

Answer 1

1) Linear tf perfect substitutes (u(x1,x2)=ax1+bx2
2) Diagramatically (quicker and easier) or using KT approach
3) Solution will be defined across 3 different intervals, for both goods; one where ratio of prices (p1/p2) equals a/b, one where it is greater, and one where it is less (eg. only good 1 will be consumed if p1/p2 < a/b tf p1 is relatively cheaper than p2)

Question 2

Check I understand and can do KT approach for Q1 PS1?

Answer 2

now

Question 3

When doing KT approach for Q1 PS1, what 4 types of conditions must be derived? And from these, how do you determine the different demand equations (and what assumption may have to be used/made?)?

Answer 3

1) FOCs, LMs, CNSTRs and CS
Assuming locally non-satiated preferences, know that BC is met with equality, therefore do 3 cases, one where the demand x1,x2»0, one where x1>0, x2=0, one where x1=0 and x2>0 - case 4 doesn’t hold since implies LNS fails tf don’t use it

Question 4

What is a leontief utility function? Where on it will a consumer maximise utility?

Answer 4

Perfect complements
ie. u(x1,x2)=min{ax1,bx2}

Where ax1=bx2

(Q2 PS1)

Question 5

What are lexicographic preferences? How do the ICs look? What is the demand function? (Q3 PS1)

Answer 5

When a consumer prefers any amount of a good, say x1, to any amount of another good, say x2

ICs in this case will be vertical lines bc. utility only increases with x1, not x2

x1(p1,p2)=m/p1

x2(p1,p2)=0

Question 6

finish these Qs on questions 4 and 5

Answer 6

now