Institute of Economic Theories University of Miskolc Microeconomics

Institute of Economic Theories - University of Miskolc Microeconomics General equilibrium Mónika Kis-Orloczki Assistant lecturer

Subject of the examination • Can a general equilibrium evolve, that could mean equilibrium in all markets, if all the economic agents would like to enforce their interests • If the resources are the same, and they have fixed amounts, and we produce only two goods from them, what allocation does ensure the Pareto-optimal inputemployment which ensures the profit-maximization.

Conditions of the examination • Economic agents aim at optimization • Convex indifference curves and isoquant curves Law of diminishing marginal utility and of diminishing returns • No externalities • The conditions of the pure competition are fulfilled

The general equilibrium of PRODUCTION without prices • 2 inputs (L, K) and 2 outputs (x, y) • Fixed quantity of input • Examination in the Edgeworth box: a graphical tool that shows the isoquant map of two products turned opposite to each other. The size of the box is determined by the quantity of the available inputs.

Edgeworth-box of production

Starting from Point D • From the point of view of the production of X, all the allocations are more efficient that are on higher isoquant curves (above D) • Same is true for Y (under D) • The area marked with blue lines: Shows allocations that are advantageous for both products Pareto-efficient combinations • There is an endless number of isoquants in the isoquant map, so when the marked area becomes only one point the 2 isoquants are tangents Pareto-optimal point, the final allocation

• In the Pareto-optimal point the slope of the tangents of the isoquant curves are equal, MRTSX = MRTSY the relative productivity of the inputs are equal in the two sectors • In a Edgeworth box there is an endless number of Pareto -optimal points • Contract curve of production(CC): Points that represent the final, Pareto-efficient input allocations, at a given quantity of input and technology. (set of all Pareto-efficient points in the Edgeworth box) • Shape of the curve is determined by the number of inputs available and by the isoquant that expresses the technology of the production.

Contract Curve of production(CC)

Production-possibility Frontier • Production-possibility Frontier (PPF) or Production possibility Curve a graph in the system of coordinates of two goods that represents the Pareto-optimal output levels at a Pareto-efficient employment of resources. Y A: Maximum output at an efficient input employment B A B: This production can’t be realized at a fixed number of inputs C: Not efficient input use or not all the inputs are employed C PPF X

Marginal Rate of Transformation • The slope of the production-possibility frontier (PPF) at any given point is called the Marginal Rate of Transformation (MRT). It shows by how many we must decrease the production of Y in order to increase the production of X by one unit. Y • The reason for the negative slope of MRT is the scarcity of resources MRT PPF 1 2 3 X • The PPF is concave the MRT is getting steeper and steeper increasing alternative costs = Law of diminishing returns

The general equilibrium of CONSUMPTION without prices • 2 consumers: A, B and 2 products: X, Y • Without prices Barter • Examination in the Edgeworth box of exchange: a graphical tool that is used to analyse the exchange of 2 goods between 2 people. It shows the indifference map of two products turned opposite to each other. The size is determined by the total quantity of available products. • During the exchange non of the actors should get on lower indifference curve, exchange that are advantageous for both consumers.

Contract Curve of exchange(CC)

Pareto efficient allocation • A Pareto efficient allocation can be described as an allocation where: there is no way to make all people better off or to make some individual better off without making someone else worse off. All the gains from trade have been exhausted or there are no mutually advantageous trades to be made. • In this point, the Marginal Rates of Substitution for both consumers are the same MRSA=MRSB. • The Pareto- efficient allocations make up the Contract Curve of the exchange. (CC)

General equilibrium of the production and exchange without prices • The same allocation is determined in two ways: – By the CC of production by input-vectors – By the PPF by output-vectors • All the points on PPF is equivalent of the points of CC, even the non-efficient points can be depicted under the PPF. • In the Edgeworth box of exchange in a Pareto-optimal point no further advantages can be gained by exchange. But by the production it can be changed: By the rearranging of the resources the amount of the available products can be changed.

• The rearranging of resources can be continued until the MRS of the consumers is not equivalent to the MRT of the production. until MRS≠MRT Y MRT PPF X

A final allocation of goods is Paretoefficient if the next conditions are true at the same time: • The exchange is effective: MRSA=MRSB • The production is effective: MRTSX =MRTSY • The criteria of the effectiveness in general: MRT= MRSA=MRSB

Prices in the model • We assume perfect competition actors are pricetakers • Income: § IA=PX*WXA+PY*WYA § IB=PX*WXB+PY*WYB (W=inicial endowment point) § ILLUSTRATION § The budget line of the cosumers are equivalent because their real income is determined by W and by the rate of prices

• The coordinates of the optimal points show the total demand of the consumer for the two goods Gross Demand: the amount of the products that the consumers would like to consume taking into account their budget constraint • The consumer possesses one part of the Gross demand wants to get the other part by exchange. This latter is called the Net Demand. • The market is not in the state of equilibrium, as the demand ≠supply at this chosen rate of prices, and the amount of the products that the consumers want to consume is not equal with the total amount of products available • New prices will evolve on the market: – Excess demand: P – Excess supply: P

• At the new price rate the amount A is willing to buy equals with the amount B is willing to sell and vice versa the sum of their Net Demand is 0. • The MRS of both consumers are equal to the market price rate, that is called equilibrium price rate: PX/PY= MRSA=MRSB • This relation can be deduced from the point of view of production as well • The market is in the state of equilibrium: » Walrasian Equilibrium » Competitive Equilibrium » Market Equilibrium

Market equilibrium • In this state in all the markets of the economy the equilibrium prices are equal with the Marginal Costs of the products. The producers’ surplus is Zero and the Consumers’ surplus is maximal. • S=D