ECO 301 – Summer 2010
Instructor: Dr. Michael Malcolm
Instructions: You can use any written materials you would like in completing this
exam, and a calculator.
Statement of academic honesty:
This exam entirely reflects my own work. I have not received assistance from
anyone or given assistance to anyone in completing this exam
Signature: _________________________________
Name:
_____________________________________
a. Anna gets an apple by paying less than it is worth to her. Bob sells his apple for exactly what it is worth to him. Anna is better off and Bob is the same. Since this exchange helps Anna without harming Bob, this is a Pareto improvement.
b. Anna gets an apple by paying less than what it is worth to her. Bob sells his apple for more than it is worth. Anna and Bob are both better off, so this is a Pareto
improvement.
c. Anna gets an apple by paying exactly what it is worth to her. Bob sells his apple for more than it is worth. Anna is the same and Bob is better off. Since this exchange helps Bob without harming Anna, this is a Pareto improvement.
d. Anna gets an apple but pays more than the apple is worth to her. Bob sells his apple for more than it is worth to him. Since Bob is better off but Anna is worse off, this is not a Pareto improvement.
e. Bob receives an apple by paying more than it is worth to him, and Anna gives up her apple for less than it is worth to her. Anna and Bob are both worse off, so this is not a Pareto improvement.
Problem 2
a. Once the price rises, the consumer still buys good 1, but can afford only 200 units and therefore obtains utility U =200. At the original prices, income would have to fall from $600 to $200 in order to achieve this decline in utility. Thus, EV =400.
b. In this case, the consumer will switch to good 2, since it is now cheaper than good 1. He can afford 150 units and obtains utility U =150. At the original prices, income would have to fall from $600 to $150 in order to achieve this decline in utility. Thus, EV =450. c. In this case, the consumer will switch to good 2, since it is now cheaper than good 1. He
a. The firm’s objective is to maximize Π subject to N =ρ
(
E+N)
. The Lagrangian is:(
, ,)
N E(
(
)
)
L=F K N E −rK W N W E− − +λ N−ρ E+N
First-order conditions: 0 L MPK r K ∂ = − = ∂ 0 N L MPN W
N λ ρλ
∂ = − + − = ∂ 0 E L MPE W E ρλ ∂ = − − = ∂
b. Solving the FOC with native labor for λ:
(
)
0 1 1 N N N N MPN W MPN W MPN W MPN W λ ρλ ρλ λλ ρ λ
ρ − + − = − = − − − = − ⇒ = −
And the FOC for expat labor:
E E
MPE W MPE W ρλ λ
ρ −
− = ⇒ =
Equating the two expressions for λ:
1
1
N E
N E
MPN W MPE W
MPN W MPE W ρ ρ ρ ρ − = − − − − ⇒ = −
a. As usual, we shift the new budget line until it hits the original indifference curve. Notice that both the income and substitution effects lower C1 for a borrower.
a. Doubling both capital and labor:
(
)
{
( )
}
{
}
{
}
(
)
(
)
2 , 2 min 2 2 , 2 2 min 2 , 2 min 2 ,
2 , 2 ,
f L K L K
L K L K f L K f L K =
= =
= <
So there are decreasing returns to scale.
b. Because of the perfect complementarity, the firm will set 2L=K. Making the substitution, we can find the input demands:
{
}
2
min ,
q K K
q K K q
=
= ⇒ =
And since 2L=K, then
2
2 2 K q
L= = . Long-run costs are then:
( )
2
2 2
30 10 25
2 LRC wL rK
q
q q
= + ⎛ ⎞
= ⎜ ⎟+ = ⎝ ⎠
c. The supply relationship for competitive firms is P=MC.
50
50
S
P MC
P
P q q
=
a. The insurance company faces a 0.1 probability of paying a $20,000 claim, so the actuarially fair premium is:
(
)
* 0.1 20, 000 2000
P = =
b. The firm collects the $1000 premium from proportion 0.9 of customers who do not suffer a loss. However, for proportion 0.1 of customers who face a loss, the firm receives a $1000 premium but pays out 20, 000−C. Setting expected profit to 0:
(
)
(
(
)
)
(
)
(
)
0.9 1000 0.1 1000 20, 000 * 0 0.9 1000 0.1 19, 000 * 0
900 1900 0.1 * 0 0.1 * 1000 * 10, 000
C C C
C C
+ − − =
+ − + =
− + =
= ⇒ =
c. For the plan in (a), the consumer always has wealth $48,000 regardless of whether he suffers a loss after paying the premium:
48, 000 219.089
A
U = =
For the plan in (b), the consumer’s wealth is $49,000 after paying the premium with probability 0.9 when there is no loss. However, after experiencing a loss, the firm reimburses only $10,000, leaving the customer with $39,000:
0.9 49, 000 0.1 39, 000 218.972
B
EU = + =
Thus, the consumer prefers the plan in (a). d. The consumer will choose plan (b) when:
0.9 49, 000 0.1 49, 000 48, 000 199.223 0.1 49, 000 219.089 0.1 49, 000 19.866
49, 000 198.66
B A
EU U
C C C
C ≥
+ − ≥
+ − ≥
− ≥ − ≥
