General Equilibrium and Efficiency

General Equilibrium Analysis is the study of the simultaneous determination of prices and quantities in all relevant markets.

General Equilibrium (GE) occurs when:

• There is no excess demand or excess supply in any output or input markets

• Consumers are maximizing utility subject to budget constraints

• Producers are maximizing profit subject to the production function

• Input suppliers are optimizing

Economic Efficiency

An efficient (or Pareto efficient) allocation of goods is an allocation in which no one can be made better off without making someone else worse off.

Conditions of Economic Efficiency

• Efficiency in exchange

• Efficiency in production

• Efficiency in the output market

Efficiency in Exchange

Efficiency in exchange occurs when

MRSA = MRSB

where MRSi = marginal rate of substitution of good y for good x for consumer i, i = A, B

= amount of good y that consumer i is willing to give up for one more unit of good x

Example: 2 consumers Ann & Bob; 2 goods X & Y

Ann is willing to trade 4Y for 1X (MRSA = 4)

Bob is willing to trade 2Y for 1X (MRSB = 2)

Ann and Bob can benefit from trading, e.g.,• If Ann trades 3Y for 1X she is better off

since she is willing to pay 4Y.• If Bob receives 3Y for 1X he is better off

since he would accept 2Y for 1X.

When MRSA > MRSB there are gains from trade. Only when MRSA = MRSB can no one be made better off without making someone else worse off, and the Pareto efficient allocation occurs.

Efficiency in Production

An allocation of inputs is technically efficient if the output of 1 good cannot be increased without decreasing the output of another good.

Efficiency in production (or efficiency in the use of inputs in production) occurs when

MRTSx = MRTSy

MRTSj = marginal rate of technical substitution of labor (L) for capital (K) for good j , j = x, y= amount by which K can be reduced when 1 more unit of L is used, so that output remains constant.

Example: Suppose MRTSx > MRTSy

e.g., MRTSx =4 and MRTSy =3

• For good x, producers can give up 4 units of K for 1 more unit of L, without changing output.

• For good y, producers can give up 3 units of K for 1 more unit of L, without changing output.

• Efficiency can be improved by using more K to produce good y and more L to produce good x.

When MRTSx = MRTSy, production efficiency cannot be improved by changing the input mix.

Efficiency in the Output Market

Efficiency in the output market occurs when

MRT = MRSA = MRSB

where MRT = marginal rate of transformation of good y for good x

= amount of good y that must be given up to produce one additional unit of good x

Example: 2 individuals Ann & Bob; 2 inputs L & K; and 2 goods X & Y

MRSA = MRSB = 3, i.e., Ann and Bob are willing to trade 3Y for 1X.

MRT = 2, i.e., the economy can give up 2 units of Y to produce 1 more unit of X.

It benefits society to produce more Y and less X until

MRT = MRSA = MRSB

MRT = MCx/MCy

where MCj = marginal cost of good j

= additional cost of producing 1 more unit of j

Example: MCx=$1, MCy = $2, MCx/MCy= ½

•The economy can produce 1 more unit of X for $1 or 1 more unit of Y for $2.•For $1, economy can produce 1 unit of X or ½ unit of Y.•The amount of Y that must be given up to produce 1 more unit of X is ½. (i.e., MRT = ½ )•MRT = MCx/MCy

Economic Efficiency Summary

Conditions of Economic Efficiency

Efficiency in exchange: MRSA = MRSB

Efficiency in production: MRTS1 = MRTS2

Efficiency in the output market: MRT = MRSA = MRSB

Note: For the entire economy, MRS must be equal for all consumers, MRTS must be equal for all firms, and MRT must be equal to MRS for all consumers .

First Welfare Theorem

The First Welfare Theorem (the Invisible Hand Theorem)

A competitive equilibrium is efficient.

A competitive equilibrium satisfies the 3 conditions for efficiency.

Efficiency in exchange: MRSA = MRSB

holds because constrained utility maximization requires

MRSA = Px/Py for Ann MRSB = Px/Py for Bob and thus,MRSA = Px/Py = MRSB

where Px is the price of good x and Py is the price of good y.

Efficiency in production: MRTSx = MRTSy

holds in perfect competition because cost minimization requires:

• MRTSx = w/r for good x• MRTSy = w/r for good y , and thus• MRTSx = w/r = MRTSy

where w = wage, r = rental rate on capital

Efficiency in the output market: MRT = MRSA = MRSB

holds because of the following. • MRT = MCx/MCy

•Px = MCx for profit maximization of firm 1 which produces good x• Py = MCy for profit maximization of

firm 2 which produces good yThese imply that:• MRT = Px/Py

For utility maximization:• MRSA = Px/Py = MRSB

Thus:• MRT = MRSA = MRSB