Econ 212

Solutions to Midterm Exam, Spring 2000

 

1. Samson=s income before tax-subsidy = 10x8+6x12 = 152 crowns

The new prices are: PbN = 10-6 = 4 crowns

PcN = 6+2 = 8 crowns

ˆ His new budget equation is: 4b + 8c = 152-30 = 122

2. a) Since U increases as x and y increase, both X and Y are goods.

b) Since U rises with x but falls with y, X is a good and Y is a bad.

c) Here y cancels out and the utility function can be written as U = 2x. Evidently, X is a good and Y is a neuter (because utility does not depend at all upon y).

3. a) MRS=-MUs/MUc=-3C/3S=-C/S

b) In equilibrium, MRS=Ps/Pc

C/S=.5/.25=2

Jane should buy twice as many chips as soft drinks.

c) Jane=s budget constraint: .5S + .25C = 5.00

Substituting for C = 2S,

S = 5

Since C = 2S, C = 2x5 = 10

ˆ Jane should buy 5 soft drinks and 10 bags of chips.

4. a) Natasha is risk-averse. To show this, assume that she has $10,000 and is offered a gamble of $1,000 gain with 0.5 probability and a $1,000 loss with 0.5 probability. Her utility of $10,000 is 3.162 . [U(I) = 100.5 =3.162].

Her expected utility of the gamble is: EU = (0.5) (90.5) + 0.5(110.5) = 3.158 < 3.162

Since EU of gamble (with same expected income) < utility from certain income, Natasha is risk-averse. Alternatively, plot the function for a few values and show that it displays diminishing marginal utility of income. Or, compute the second deriva tive of the utility function and show that it is negative implying diminishing marginal utility.

b) The utility of her current salary is 100.5 = 3.162.

The EU of the new job is: EU = (0.5) (50.5) + (0.5) (160.5) = 3.118 < 3.162

Therefore, she should not take the new job.

c) We know the EU of the gamble is 3@118. Substituting into her utility function, we have 3.118 = I0.5. Solving for I, we find that the certainty equivalent of the gamble is $9,722. Thus, the maximum amount Natasha would be willing to pay for insurance is $10,000 - $9,722 = $278.

5. Under Bank 1's offer: value of $1000 after 3 years = 1000 (1+.08) (1+.08) (1+.11).

Under Banks 2's offer: value $1000 after 3 years = 1000 (1+.11) (1+.08) (1+.08).

ˆ Both offers are equally valuable and Bank 2's claim is false.

6. Higher wage for overtime work would produce no income effect. There would be only substitution effect which would induce workers to work more. See pp. 175-6 of Varian for details with diagram (Fig 9.10)