Question

1. Why might some prefer a prix fixe (fixed price) dinner costing about the same as an à la carte one (where you pay individually for each item)? (Assume the food is identical.)

2. Consider a person with the following utility function over wealth: u(w) = e^w, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has a 40% chance of wealth of $100,000 and a 60% chance of wealth of $2,000,000 as summarized by P(0.40, $100,000, $2,000,000).

a. What is the expected value of wealth?

b. Construct a graph of this utility function (recall your excel?).

c. Is this person risk averse, risk neutral, or a risk seeker?

d. What is this person’s certainty equivalent for the prospect?

3. Consider two prospects.

Problem 1: Choose between

Prospect A:	$2,500 with probability	0.33
	$2,400 with probability	0.66
	Zero with probability	0.01
Prospect B:	$2,400 with probability	1.00

Problem 2: Choose between

Prospect C:	$2,500 with probability	0.33
	Zero with probability	0.67
Prospect D:	$2,400 with probability	0.34
	Zero with probability	0.66

It has been shown by Daniel Kahneman and Amos Tversky (1979, “Prospect theory: An analysis of decision under risk,” Econometrica 47(2), 263-291) that more people choose B when presented with problem 1 and when presented with problem 2, most people choose C. These choices violate expected utility theory. Why?

Answer 1

Answer:

1)

Some prefer fixed price dinner over a la carte, while both costing the same and food is being identical. The reason is that because fixed price dinner has an upper limit of cost and unlimited food, therefore perceived value of the fixed price dinner is high as compared to a la carte. Consumers prefer value for money deals. Fixed price dinner also offers the comfort and convenience of not going through the hassle of selecting items from the a la carte menu to suit the budget. It usually applies to price sensitive customers.

2)c) Risk seeker, because the graph is convex

a. Solution E(w) .4.5 + .6 * 10 = 6.2 UP) = .4e-6e10-13,216.54 0.50 b. 25000 20000 15000 10000 5000 0 10 1 0 2 4 6 Hundreds of thousands of dollars The function is convex.

d) e^w = 13,216.54 gives w = 9.4892244 or$948,922.44

3)

This is an example of the Allais paradox.

The first choice suggests that ;

u(2,400) > 0.33u(2,500) + 0.66u(2,400) or 0.34u(2,400) > 0.33 u(2,500)

while, the second choice suggests just the opposite inequality.

This can simply be understood by the following image:

$2,500 0.33 (D: 100% $2,400 $2,400 (e).く066 0.01 S0 $2.400 0.34 $2,500 0.33 0.66 0.67 s S0

In other words;

u(2400) > 0.33u(2500) + 0.66u(2400) + 0.01u(0)

u(2400) > 0.33u(2500) + 0.66u(2400)

deducting 0.66u(2400)

0.34u(2400) > 0.33u(2500)

Similarly;

Reversing in second case;

0.34u(2400) < 0.33u(2500)

Hence, looking from the diagram also, it can be said that (e) is preferred in first case and (g) from the second.