Lecture 5 - Optimal Choice

Question 1

If preferences are monotonic, does the optimal preference lie on the budget line? Why or why not?

Answer 1

• yes
• as monotonicity means that the consumer can become better off by consuming more of a good

Question 2

What will the consumer do if (MU1/p1) > (MU2/p2)?

Answer 2

• good 1 gives more utility for each pound spent
• so they will sell good 2 to buy good 1 instead (if they have any good 2 to sell)

Question 3

What will the consumer do if (MU1/p1) < (MU2/p2)?

Answer 3

• good 2 gives more utility for each pound spent
• so they will sell good 1 to buy good 2 instead (if they have any good 1 to sell)

Question 4

If MU1/MU2 were less than p1/p2, what would the consumer do?

Answer 4

sell good 1, buy good 2, and be better off

Question 5

If MU1/MU2 were greater than p1/p2, what would the consumer do?

Answer 5

sell good 2, buy good 1, and be better off

Question 6

Give the complete scheme of how to find optima when given the utility function and the budget set?

Answer 6

• either an optimum is a corner point
• or it is an interior point, then use 2 conditions:
• 1) MRS = -p1/p2
• 2) monotonicity: p1x1 + p2x2 = m
• identify corner points
• identify all points satisfying 1) and 2)
• find a point(s) that yields the maximal utility

Question 7

If preferences are convex, and there exists a point whereby MRS = -p1/p2 and monotonicity: p1x1 + p2x2 = m, is it guaranteed to be an optimum? Why or why not?

Answer 7

• it is guaranteed to be an optimum
• as