Choice under uncertainty

Question 1

What is the expected value equation used for expected utility

Answer 1

Question 2

How could we describe the utility of income

Answer 2

• Diminishing marginal utility of income
• At higher incomes, value of pound becomes smaller

Question 3

What does diminishing marginal utility of income imply and explain using this graph

Answer 3

• Given the graph which is concave
• The midpoint, 40, of two values 10 and 70 has a utility of 32 which is higher than 28 the average utility at 10 and 70
• So we prefer 40 with certainty than a 50 50 chance of 10 or 70

Question 4

What is a fair gamble

Answer 4

A gamble with expected value of zero

Question 5

What does risk averse mean

Answer 5

Preferences described by a utility function with diminishing utility of wealth

Question 6

Risk seeking explanation

Answer 6

Preferences described by a utility function with increasing marginal utility of wealth

Question 7

Risk neutral explanation

Answer 7

Preferences described by a utility function with constant marginal utility of wealth

Question 8

What shape is the utility function of a risk seeking person

Answer 8

Convex

Question 9

How does a risk seeking person react to a fair gamble

Answer 9

• If they refuse the gamble and choose certain income, the expected utility on the utility function is below that if they were to accept the gamble
• Mid point on straight line between two points on curve is higher utility than if on the curve

Question 10

What does a risk neutral person do to maximise expected utility

Answer 10

They maximise expected value

Question 11

How can consumers respond to risk

Answer 11

By risk pooling and distributing the losses/gains equally as it reduces uncertainty thanks to law of large numbers

Question 12

Explain the reservation price for insurance using the diagram

Answer 12

• The certainty equivalent which gives the same utility as the gamble is 370 in this case
• Starting off with income of 700, so 700-370 means reservation price for insurance is 330
• For the company their ‘fair ‘ price is 200 and they receive this and in return provide certainty, eg at 500m, utility on curve (certainty) is 33 whereas without the expected utility is only 30