Question

1)

(a) You role a normal six sided dice. What is the expected value of that role? (b) Emma’s utility function, holding prices constant, can be expressed in terms of her income: U = I^2 . Is Emma risk loving, risk neutral, or risk adverse. Why? Show with a specific example.

2)

Autumn’s utility curve is defined as: U(c, s) = c^1/2*s^1/2 , where c is the consumption of cars and s is the consumption of shoes. The price of car is set at $2 while the price of shoes is $4. Autumn has 20 dollars to spend on consumption.

(a) Draw this budget constraint.

(b) Find the equilibrium point. Draw it and the IC on the graph.

(c) Assume the price of cars increases to that of the price of shoes. Find the change in the consumption of cars.

(d) What is the utility level in this new equilibrium?

(e) From your answer in part c, how much of this change is the income effect? How much is the substitution effect? (Hint: Graphing may help.)

(f) From parts a through e, are cars and shoes complements, substitutes, or neither? Why?

Answer 1

1.

(a) A six side dice is rolled then total outcomes are 6 and the expected value of the roll is

E(X)= where x is the outcome on the dice and P(X) is the probability of each event which is 1/6 for each outcome on the roll of a dice.

E(x) =21/6 =7/2

(b) If U=I^2 which represents a convex function means extremes are preferred to average value hence Emma would be risk loving in this case.

2.

Given U=c^1/2 * s^1/2 and pc= 2, ps= 4 and m=20 then the budget line will be pc.c+ps.s=m

(a) 2c+4s=20 implies

c+2s=10

(b) At tangency point,

MRS=pc/ps

s/c =2/4

c=2s using in budget constraint implies

2c=10

c=5 and s=2.5

(c) if pc=4 then budget line will be 4c+4s=20

c+s=5

at tangency point, c=s and then c=s=2.5

(d) new utility will be

u(2.5,2.5) = 2.5