Exchange No production. Individuals are `born with' goods that can be consumed or traded. Lecture April 7. Welfare and markets.

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1 Lecture pril xchange No production. Individuals are `born with' goods that can be consumed or traded. elfare and markets. ssume: Two persons nna () and rewster () Two goods, and with the prices g and w. nna's initial endowments of the goods: and = = rewster's initial èndowments' of the goods: and = = tility functions: = = rewster = = rewster = = = = oint gives the initial endowment, how many goods they have at the beginning. e draw the indifference curves of nna nna nna = = = = nd here is the indifference curves of rewster. Since they have the same utility functions the indifference curves will mirror each other. nna rewster = = = = = = = = = = raw the indifference curves that passes through the initial endowment, that is all allocations that gives the utility of. How many would nna need to reach a utility of at different numbers of?

2 = = = = Here we also have the indifference curves that passes through the initial endowment. nna rewster = = = = The blue area is allocations that nna would prefer towards the initial endowment since that area are above the initial indifference curve nna rewster = = = = This blue area shows allocations that rewster would prefer nna rewster = = = = This blue area shows allocation that both nna and rewster would prefer. Here is clearly a possibility of a areto improvement. nna rewster = = = = rewster ssume that nna gives one unit of to rewster and gets one unit of in exchange. e move to point. oth individuals are better of. nna = = = = ut there are still possibilities for improvement. This blue are shows allocation that both nna and rewster prefer to point. nna rewster

3 = = = = xchanging more units moves us to point C. nna rewster C = = = = t point C there are no allocation that both persons would prefer, we have a areto efficient allocation of the goods. nna rewster C tility before exchange: = = = = = = = = oth persons are better of. tility after exchange: If I have something that you like very much and You have something that I like very much we would benefit from exchange. t point C the slope of the indifference curves are the same for both individuals. MRS are the same for both persons, their valuation of another unit of in terms of good are the same. t point the slope of the indifference curve where not the same. The two persons made a different valuation of the goods. nna put higher value of in units of than rewster did. (nd rewster put higher value on in units of ) Only when MRS differ between two parties there is a potential gain in exchange. On a free market with rational individuals, exchange will continue until MRS is equal for all consumers. = = = = The contract curve shows all points where MRS are equal for both individuals. fter exchange we will end up somewhere on the contract curve. nna rewster The areto Criterion: If we can do something that make one human better of without harming anybody else that should be done. If there are no possible areto improvements the situation is areto efficient. If we are on the contract curve no changes can be made to improve for one person without harming the other. ll allocations on the contract curve are areto efficient The First Theorem of elfare conomics free market with rational individuals gives a areto efficient outcome. (If we do not have any market failures.) The Second Theorem of elfare conomics If the initial endowment point changes, the equilibrium point will change. ctually, any point on the contract curve can be reached by an appropriate choice of initial endowments.

4 The initial endowment gives us a fraction of the contract curve that can be reach. rewster Let us investigate the impact from the preferenses =,,, =, Once again we draw the indifference curves of nna rewster nna nna rewster rewster =,, =,, = =,,,, Once again we draw the indifference curves of nna- nd then we add the indifference curves of rewster. nna The contract curve passes through points where nna has a lot of and rewster a lot of. nna =,,, =, ssume the initial endowment was units of each good for each person (point ). Once again they benefit from exchange, this times because they have different tastes. (ifferent preferences) nna rewster Markets with perfect competition in the dgeworth box Now we introduce prices and move from barter to trade (payments) (ssume that there are million nna's and million rewster's, so that each of them takes the price as given) ith prices in the modell nnas ndowment of goods corresponds to a sum of money, her income. She sell these goods and by another combination of good that costs exactly the same. Her budget constraint will be: + = + The left hand side is the money she gets from selling her initial endowment, the right had side the cost of the goods she buys. e can draw the budget restriction as a straight line in the figure: (To se this solve for ) = +

5 Markets with perfect competition in the dgeworth box To get the relative price of the market we use the fact that:. On a free market with perfect competition the relative price in equilibrium will always equal MRS. If nna uses the money she gets when selling her endowment to buy her final consumption these two points must be situated on the same price line. (Her budget constraint). Therefore we can draw a line that passes through the initial point and that passes through the contract curve in a point where the slope of the line is equal to the slope of the indifference curves. =,,, =, ssume the initial endowment was units of each good for each person (point ). The prices on the market gives us the point on the contract curve where we find the equilibrium. The relative price should be equal to MRS, (in this case equal to ). nna rewster =,,, =, rewster nna: =,, This cannot be a market equilibrium since relative price differ from MRS. t this relative price the will buy different combinations of goods. ssume both prices are equal to and that both persons have an income of nna would buy and nna rewster: ssume both prices are equal to and that both persons have an income of rewster would buy and,, =,, =,, =,, =,, =, =,, =, = = = =,,,, =, =, oth persons are better of. tility before trade: tility after trade: If I have something that you like very much and You have something that I like very much we would benefit from exchange.

6 Lets have a look at edgeworth.xlsx that you should use in the computer exercise arbage disposal roduction ossibilities Frontier (F) production possibility frontiers shows the combinations of and that are possible to produce with available amount of Capital and Labour. n interior point like point is inefficient since it is possible to increase the production of one goods without decreasing the production of the other. (e would be in such a point if we have a large unemployment.) ine arbage disposal roduction ossibilities Frontier (F) F ll points on the frontier are efficients since we cannot increase the production of one good wothout decreaseing the production of the other. (Here we use all available labour and capital.) The (negative of the) slope of the F is called the Marginal Rate of Transformation (MRT). It describes how much more we get if we reduce by one unit arbage disposal hy do MRT differ? ssume some workers are better on collecting garbage while other workers are better at producing wine. t F where we produce equal amount of and everyone can produce the things they are best to produce F If we increase production of ine and reduce production of garbage disposal we can move a worker that are almost equally good at both kind of production. ine ine arbage disposal hy do MRT differ? t point F even those that are good at wine production and bad in producing garbage disposal work with garbage disposal. If we increase production of ine and reduce production of garbage disposal we can move a worker that better at wine production than on garbage disposal. Thus we can increase production of F wine a lot without loosing that much garbage disposal. hy do MRT differ? t point even those that are good at garbage disposal and bad in producing wine work with wine production. arbage disposal F If we increase production of wine and reduce production of garbage disposal we must move a worker that is better at garbage disposal than on wine production. Thus we can increase production of wine a little but loosing a lot of garbage disposal. ine ine

7 rofit maximization rofit maximization Firms cannot produce more of the goods than what the production possibility frontier allow but they can choose different points on the frontier. hat point will maximize profits? Total profit is equal to: = + e may draw this as a straight line in the figure. = + The higher the larger intercept will this straight line have. arbage disposal + C In this figure I have drawn three different Isoprofit curves all corresponding to the same relative price but different profit levels. n isoprofit curve shows different combinations of the two goods that gives the same profit. The higher isoprofit curve the higher is the profit. t point C profit is maximized. No higher isoprofit curve is possible to reach from this production possibility frontier. The three lines has the same slope since the slope is given from ine fficiency eneral equilibrium It is optimal for firms to produce where = (If not profit could be increased by changing the mix of output. ssume for example that MRT =, while =. Reducing with unit reduces profit with $ but increasing with one unit increases profit with $.) arlier we showed that consumers maximize utility when: = t optimum MRT = MRS The opportunity cost of producing one good in terms of the other good, is exactly equal to the consumers valuation of that good in terms of the other good. arbage disposal e can illustrate the general equilibrium in the figure using an indifference curve ut what mechanism give us the right price? ine arbage disposal hy do we reach an optimum? C ssume that prices where different Consumers want to buy more wine than what is produced. On the other hand producers produce more arbage disposal than what they sell. The price of wine will increase and the price of arbage disposal will fall. quilibrium in two markets, illustrated with demand and supply e expect gasoline and ethanol to be substitute since you can drive your car on both fuels. ssume there is a decrease in the marginal cost of producing ethanol due to a technological break through. The supply curve shifts downwards to the right The price of ethanol decreases. Market for gasoline Market for ethanol S S S ine e can produce wherever we want on the production possibility frontier but we must consume in the same point (at least without international trade) On a free market we will consume the combination of good that maximize utility. In that point MRS = MRT.

8 quilibrium in two markets, illustrated with demand and supply Since gasoline and ethanol are substitutes a lower price of ethanol reduces demand of gasoline. The price of gasoline decreases quilibrium in two markets, illustrated with demand and supply Since gasoline and ethanol are substitutes a lower price of gasoline reduces demand of ethanol. The price of ethanol decreases. Market for gasoline Market for ethanol Market for gasoline Market for ethanol S S S S S S quilibrium in two markets, illustrated with demand and supply Since gasoline and ethanol are substitutes a lower price of ethanol reduces demand of gasoline. The price of gasoline decreases Market for gasoline Market for ethanol S S S