INTERMEDIATE MICROECONOMICS

5. General Equilibrium

GENERAL EQUILIBRIUM
(under construction)

- how to link individual consumer, firm and market to economy as a whole

- Partial Equilibrium Analyses investigate changes in one market assuming that conditions in other markets do not change.

- General Equilibrium Analyses investigate changes in ways that include interrelationships with other markets and changes that might occur there.

- basic assumption: perfect competition
 

1. GENERAL (M&Y 10th Fig. 16.1; M&Y 11th Fig. 16.1; B&B Fig. 16.4; B&Z not displayed)

• All factors of production are owned by consumers and each consumer supplies inputs of capital (K) and labour  (L) according to their preference.   All output  (x, y) is produced by firms according to their profit maximization possibilities. 

• The quantity of K & L is fixed.  The maximum amount of x or y that can be produced using K & L is fixed with all possible combinations of x & y that can be produced defining a production possibility frontier (see point 7 below).

• Consumers choose preferred market baskets subject budget constraint.   It is assumed that an initial distribution of income exists and prices are fixed.  Conditions for consumer equilibrium:

• the Marginal Rate of Substitution (MRS = MUy/MUx) equals the slope of the Budget Line ;

• the MRS also equals -1/(/Px/Py); and,

• a 'rationale' consumer will equate the MU per dollar of each commodity consumed, i.e. MUx/Px = MUy/Py .

• Every firm maximizes profits subject to constraints fixed by technology, demand for product and price of inputs.   Conditions:

• MC = MR = P

• Long Run Economic Profits are zero for every firm.

• The quantity demanded equals the quantity supplied for all products and inputs.

2. EXISTENCE

• The Existence of General Equilibrium has been “proven” - theoretically.

• This existence can be illustrated by counting equations and variables that characterize equilibrium.

• This counting procedure is not, however, the proof.
 

3. EDGEWORTH BOX FOR CONSUMPTION (M&Y 10th Fig. 16.2; M&Y 11th Fig. 16.2; B&B Fig. 16.3; B&Z not displayed)

• Edgeworth Box  for consumption reflects allocation of fixed supplies of goods between consumers (M&Y 10th Fig. 16.4, M&Y 11th Fig. 16.3;  B&B Fig. 16.15; B&Z not displayed) assuming initial income distribution

• Exchange between consumers represented by movement within Edgeworth Box
 

4. CONTRACT CURVE IN CONSUMPTION (M&Y 10th Fig. 16.2; M&Y 11th Fig. 16.2; B&B Fig. 16.3; B&Z not displayed)

• Gven initial income distribution (at P) off contract curve, MRS for consumer different allows for Pareto optimum change making one person better off without making the other worse off; outcome depends on bargaining power of the parties

• Exchange equilibrium where there is equality in the Marginal Rates of Substitution, i.e., MRS of consumer 1 = MRS of consumer 2 (or more)

• The Contract Curve highlights all points within an Edgeworth Box that can serve as Exchange Equilibria,  i.e., all points for which the MRS of both people are equal or all points for which the indifference curves of both people are tangent to one another.

5. EDGEWORTH BOXES FOR PRODUCTION (M&Y 10th Fig. 16.3; not displayed M&Y 11th, B&B, B&Z)

• Given inital endowment of factors off contract curve (z), MRTS for producers different allows for Pareto optimum exchange making one producers output higher without lowering output of the other

• Edgeworth Boxes illustrates allocation of fixed supplies of inputs between the production of two types of goods.

• Equilibrium in Production is achieved when the Marginal Rates of Technical Substitution in the production of the goods are equal (M&Y 10th Fig. 16.5; M&Y 11th Fig. 16.5; B&B Fig. 16.17; B&Z not displayed).

6. CONTRACT CURVE IN PRODUCTION

• The Contract Curve in a Production Edgeworth Box highlights all points that can serve as Exchange Equilibria between the production of two goods,  i.e., all points for which the MRTS in the production of both goods are equal or  all points for which the isoquants of both goods are tangent to one another (M&Y 10th Fig. 16.5; M&Y 11th Fig. 16.5; B&B Fig. 16.17; B&Z not displayed).

7. CONTRACT CURVE AND THE PRODUCTION POSSIBILITY FRONTIER

• Points on this Contract Curve identify combinations of outputs for two goods that support a Production Possibility Frontier (M&Y 10th Fig. 16.6; M&Y 11th Fig. 16.6; B&B Fig. 16.18; B&Z not displayed).
 

8. MARGINAL RATE OF PRODUCT TRANSFORMATION

• The Marginal Rate of Product Transformation reflects the rate at which an economy can transform one good into another by reallocating inputs along a contract curve (M&Y 10th Fig. 16.7, M&Y 11th Fig. 16.7; B&B  & B&Z not displayed).

• The MRPT is the slope of a Production Possibility Frontier at a specific point.
 

9. OPTIMALITY

The optimal allocation of inputs picks a point of the Frontier for which the underlying Exchange Equilibrium can support a common MRS for consumption that equals the MRPT,  i.e., the Marginal Rate of Product Transformation.

10. SUMMARY

• general equilibrium occurs when there is a simultaneous equilibrium in all markets assuming perfect competition

• in production, exchange equilibrium (between inputs) exists where producers of different goods share the same MRTS (contract curve in production)

• from the contract curve in production, the PPC can be derived

• in consumption, exchange equilibrium (between goods) exists where consumers share the same MRS (contract curve in consumption)

• from the contract curve in consumption, the point of production on the PPC will be where the MRPT (slope of PPC) equals consumer MRS between goods (contract curve in consumption) assuming an initial distribution of income (goods) between consumers