2 - Partial Equilibrium

Question 1

How to draw an indifference curve?

Answer 1

1) Take utility function
2) reformulate in terms of m (numeraire) =
3) first derivative: curve is increasing (+) or decreasing (-)?
4) second derivative: curve is concave (+) or convex (-)?

Question 2

What is the marginal rate of substitution (MRS xy)?

Answer 2

How many units of y would you give up for an additional unit of x?

Question 3

How to compute the marginal rate of substitution (MRS y) in a partial equilibrium?

Answer 3

Take the negative slope of the indifference curve (=-f.o.c.)

Question 4

How to derive the consumer’s demand function?

Answer 4

Maximized m and x in the utility function (f.o.c.) subject to the budget constraint

Question 5

How to draw a production set?

Answer 5

Draw the production function (usually given) to the right (negative m!)

Question 6

How do you compute the production costs in partial equilibrium?

Answer 6

Solve the production function for m => c(y) = function of y

Question 7

How to derive the supply function?

Answer 7

Maximize y in the profit function ( = revenue - cost)

revenue: p y
cost: m = c(y)

Question 8

How to get market equilibrium?

Answer 8

supply = demand
x* = y(p)

Question 9

What is the numeraire?

Answer 9

• all other goods as a single composite commodity
• “Numeraire is an economic term that represents a unit of account. A numeraire is usually applied to a single good, which becomes the base value for the entire index or market. By having a numeraire, or base value, it allows us to compare the value of goods against each other.”

Question 10

Why is a production vector negative?

Answer 10

Because it models input (positive vectors are output!)

Question 11

What is the aggregate surplus?

Answer 11

“value produced in the economy”, sum of consumer and producer surplus:
Σϕᵢ(xᵢ(p)) - Σcⱼ(yⱼ(p))

Question 12

What is the consumer surplus? How do you calculate it?

Answer 12

How much consumers would be willing to pay for
the consumption of xᵢ in excess of paying pxᵢ:
Utility (=average willngness to pay for the good) - price to pay for the x units of the good.

Question 13

What is a partial equilibrium?

Answer 13

market for one specific good in isolation

Question 14

What are the assumptions in the partial equilibrium approach?

Answer 14

1) if the good has only a small share in overall consumption then welfare effects are negligible and the effect on other market prices are negligible
2) all other goods are treated as a single composite commodity, the numeraire m
3) economic allocation: (x, y, mₓ, mᵧ)

Question 15

What are the 3 equilibrium conditions?

Answer 15

1. Profit maximization: p = c’ⱼ(yⱼ)
2. Utility maximization: ϕᵢ’ (xᵢ) = p
3. Market clearing: Σxᵢ = Σyⱼ -> only one clearing condition due to Walras’ Law

Question 16

What is the first fundamental welfare theorem?

Answer 16

the “Invisible Hand Theorem”: any competitive market equilibrium leads to a Pareto efficient allocation of resources. I.e. If the price p* and allocation (x,y,mₓ,mᵧ) constitute a competitive equilibrium, then it is Pareto optimal.

The main idea here is that markets lead to social optimum. Thus, no intervention of the government is required, and it should adopt only “laissez faire” policies. However, critics say that the assumptions for this theorem are rarely seen in real life.

Question 17

What is the second fundamental welfare theorem?

Answer 17

With market mechanisms for redistribution, any efficient allocation can be attained by a competitive equilibrium (= separation of efficiency and distribution). I.e. wealth redistribution policies.

Any Pareto optimal levels of utility (u₁,…,uₗ) can be sustained by a competitive equilibrium outcome via an ex ante redistribution of the numeraire. -> If we don’t like the outcome (equity considerations?), we redistribute income in a “clever way” before the market starts. Separation of efficiency and rent sharing.

Question 18

What is the economic allocation in the partial equilibrium?

Answer 18

Economic allocation: (x,y,mₓ,mᵧ)

Question 19

What does quasi-linear utility assume? (3 properties of utility)

Answer 19

1) ϕ’ᵢ(x) > 0; (utility is strictly increasing with x, positive slope)
2) ϕ’‘ᵢ(x) < 0; (utility increases less and less, concave)
3) ϕᵢ(0) = 0 (utility is zero without any goods)

Question 20

What is the market equilibrium in terms of aggregate demand and supply?

Answer 20

Σxᵢ(p) = Σyⱼ(p)

Question 21

What is Walras’ law?

Answer 21

a market is in equilibrium if the other L-1 markets are in equilibrium

Question 22

How to achieve pareto optimality?

Answer 22

maximize: Σϕᵢ(xᵢ) + ωₘ - Σcⱼ(yⱼ)

under feasibility condition: Σxᵢ = Σyⱼ

Question 23

What is the producer surplus?

Answer 23

The shaded area between price line and supply function in the D&S graph. Can be calculated in 2 ways:

LINEAR SUPPLY:
triangle formula ( side x side / 2)
side 1: price
side 2: slope of supply function * price

NONLINEAR SUPPLY:
take integral for supply function, calculate area between 0 and p.

Question 24

What is the budget constraint for the consumer?

Answer 24

The sum of the prices of the bought goods must be equal to or smaller than the initial endowment + ownership share of profit (if private ownership economy).
E.g. in two good economy: pₘm + pₓx =< ωₘ + ωₓ

Question 25

What is an interior solution?

Answer 25

Interior solution:

m >0, x > 0

Question 26

What is a corner solution?

Answer 26

Corner solution:

x = 0 or m = 0

Question 27

What is partial equilibrium analysis?

Answer 27

where we look at the determinants of price and quantity in a particular market holding all other markets constant. Usually, we study the behavior of the markets using the traditional supply and demand framework. Through the use of supply and demand, we have determined the equilibrium price and equilibrium quantity in different types of markets.