Midterm 2

Question 1

Perfect complements

Answer 1

U = Min(aq1, bq2)
D1 = y/(p1 + p2)
Consume in ratio aq1 = bq2

Question 2

Perfect substitutes

Answer 2

U = q1 + q2
D1  = y/p1 if p1

Question 3

Cobb douglas

Answer 3

u = q1^a q2^b
D1 = a/(a+b) y/p1

Question 4

Walras law

Answer 4

if the market for good 1 is in equilibrium, so is the market for good 2

Question 5

If preferences are convex…

Answer 5

there is at least 1 eq and it is paretto efficient

Question 6

Abs(MRS) > Abs(MRT)

Answer 6

value good 1 more, should consume more of good 1 to increase utility

Question 7

relative prices

Answer 7

if p1 and p2 are equilibrium prices, then so are kp1 and kp2

Question 8

Calculating equilibrium from production

Answer 8

1. Firms: maximize profit = p f(l) - wl (set derivative = 0), use to find q produced, plug in to find profit
2. Consumers: find demand with utility function, y = labor income + 1/2(profit1 + profit2)

Question 9

finding contract curve

Answer 9

A MRS = B MRS
q1 B = total endowment of good 1 - q1 A
q2 B = total endowment good 2 - q2 A
Plug in, cross multiply, solve

Question 10

Pareto efiicient

Answer 10

an allocation is Pareto efficient if no other allocation gives at least as high of utility to every consumer of strictly higher utility to some consumer

Question 11

1st welfare theorem

Answer 11

Equilibria are Pareto efficient

• in equilibrium, both MRSs = price ratio
• assumes: price taking, complete markets, no externalities

Question 12

2nd welfare theorem

Answer 12

If preferences are convex, lump sum transfers of initial endowments can make any point on the contract curve and equilibrium

Question 13

Arrow’s axioms (efficiency/welfare)

Answer 13

1. Pareto efficiency: if everyone prefers x to y, so does society
2. No Dictatorship: there is no single individual such that society’s ranking is always this individual’s ranking
3. Independence of Irrelevant Alternatives: society’s ranking of x and y only depends on rankings of x and y and not other alternatives

Question 14

CV

Answer 14

change in income required to get old utility with new prices

Question 15

EV

Answer 15

change in income required to get new utility at old prices