Chapter 5.4 - Walras Law and Relative Prices - YouTube

hi this is the fourth video of chapter five  general equilibrium and economic efficiency  

in this video we are going to talk  about walgreens law and relative prices

we say yes to begin

we know that in a two-person exchange the  outcome can depend on the bargaining power  

of the two parties however competitive  markets have many buyers and many sellers  

so if people do not like the terms of an  exchange if they don't want to trade with some  

specific buyer or seller they can look  for another seller who offer better terms

so as a result each buyer and each seller is going  to take the price of the goods as fixed so they  

are price takers and they just have to decide  how much to buy or how much to sell at these  

prices we can show how competitive markets lead  to efficient exchange by using the headquarter  

box to mimic a competitive market okay so if  we have the eighth or box we can mimic this  

competitive mark this perfect competition that  we studied in in the first chapter this slide  

is going to show the opportunities for trade  when we start at the location given by the point  

a okay so we are starting from here and when  the prices of both both food and clothing  

are equal to one i mean not the actual prices  but the relative prices it is the price of one  

good divided by the price of the other group so  if the price are equal the prices of both goods  

are equal then the relative prices will be one so  the actual prices don't matter what matters is the  

price of food related to the price of clothing  when the prices of food and clothing are equal  

each unit of food can be exchanged for  one unit of clothing as a result the price  

line which is pp prime this is the price line  in the diagram has a slope of -1 because it will  

be exchanged one by one and it describes all  possible allocations that exchange can achieve  

so let's suppose that we have many  games and many currents in our market  

and each james is in our market is going to decide  to buy two units of clothing and sells two units  

of food in exchange so this is going to move him  from a to c okay from the point a to the point c  

there will be an increase in satisfaction because  we will change from the indifference curve  

u j1 to u j2 so we will pass to another  utility another utility function another not  

utility function sorry but indifference card  so this will be a new indifference car which  

is farther from the region for james so he will  be better in a better situation in c than in a  

in the meanwhile each current is going to buy  two units of food and sells two units of clothing  

and this will move hair or each current from a  to c so she all day all the currents are going  

to increase their satisfaction because they  will change from this utility function uk1  

from util from this one to the one which is uk2  which is in c or it pass through the point of c  

okay so she will also increase hair utility from a  to c from uk 1 to uk2 so we choose prices for the  

two goods so that the quantity of food demanded  by each current in this market is equal to the  

quantity of food that each james wishes to sell  and the quantity of clothing demanded by james  

is equal to the quantity of food that each garden  wishes to sell and as a result the market for food  

and clothing are in equilibrium so here we will  we will have an equilibrium an equilibrium is  

a set of prices at which the quantity demanded  equals the quantity supplied in every market so  

here we will find an equilibrium as we can  see for both karen and james because their  

their utility their indifference card are tangent  here and they are also tangent to the price line  

however not all the prices are consistent with  an equilibrium for example if the prices of food  

is 1 and the price of clothing is 3 food must  be exchanged for clothing on a 3 to 1 basis  

but then each james would be unwilling to trade  any food to get additional clothing because his  

or their marginal rate of substitution of clothing  for food if you remember from the past slides was  

0.5 one half each cutting on the other hand would  be happy to sell clothing to get more food but  

she has no one to trade with so the market will  be there for in this equilibrium because the  

quantity demanded is not equal to the quantity  supplied so we will have a this equilibrium  

and this equilibrium should only be temporary  because in a competitive market prices will adjust  

if there is excess demand in some markets this  means that the quantity demanded of one good  

is going to be greater than the quantity supply  and there will be excess supply in others which  

means that the quantity supply will be greater  than the quantity demanded so with our example  

each currency month for food is going to be  greater than each james willingness to sell it  

at a price of one over three the relative  price was one over three so whereas each  

current willingness to trade clothing is greater  than each james demand for it as a result of this  

excess demand for food and excess supply of  clothing we will expect the price of food  

to increase relative to the price of clothing  and as the price the prices are changing  

the demands of all the people who are in the  market will change as well so eventually the  

prices will adjust until an eclipsing was rich so  if we find it is equilibrium in the beginning and  

we have a competitive market at the end we will  find an equilibrium because the prices will adjust  

at some point so therefore there is a difference  between an exchange with only two people and  

an exchange with many people involved when  we have competitive a competitive market  

if there are only two people if we have only two  traders the bargaining process is going to leave  

us an indeterminate outcome outcome however  when we have many people involved in the market  

the prices of the goods are going to be determined  by the combined choices of demanders and suppliers  

of good so we can see that the point c is  an allocation that is efficient as i as i  

have said it is a competitive equilibrium which  is efficient the indifference curve are tangent  

okay so just to continue the the idea that we  have just explained is illustrated by a adam smith  

with his invisible hand and this will be the  third theory of wealth for economics if everyone  

trades in the marketplace and all mutually  beneficial traits are completed the resulting  

equilibrium allocation will be economically  efficient so let's summarize what we know about  

a competitive equilibrium from the consumer's  perspective first because the different carbs  

are changing all marginal rates of substitution  between consumers will be equal and second because  

each indifference car is tending to the price  land each person marginal rate of substitution  

of clothing for food is going to be equal  to the ratio of prices of the two groups

okay so we will have this at marginal  rate of substitution for james  

between food and clothes will be equal to  the a price line to the relative prices  

and it will be equal to the marginal rate  rate of substitution for car which between  

food and growth which means  that we are in equilibrium okay

okay so just to continue in this slide we  put the information from the network box  

in a different form here we have james utility  in this axis in this horizontal axis and  

in the vertical axis we have currency utility  

any point in the s4 box corresponds to a point  in its figure because every allocation generates  

utility for both people and every movement to the  right everyone to the right is going to represent  

an increase in james utility and every movement  upward is going to represent an increase in  

current utility so the utility possibilities  frontier represents all allocations that are  

efficient and we see that e f and g are obviously  points from the contract curve so they are all  

efficient all the points that are on this curve  are efficient in this utility possibility frontier  

and then the point h will represent an inefficient  allocation h is not efficient it's inefficient you  

have it here in the text and then we have l we  see which is not attainable it's not attainable  

because there is not enough goods to generate  the levels of utility that this point represents  

so the utility possibilities frontier then is  going to describe all efficient allocations  

of resources measured in terms of the utility  levels of two individuals and in economics we  

often use a social welfare function to describe  the well-being of the society as a whole  

in terms of the utilities of individual members  and then this is extracted from the first  

slide the walrus law is an economic theory which  states that the existence of excess supply in one  

market must be matched by excess demand in another  market so that both factors are balanced out  

so the wireless law asserts that an  examined market must be in equilibrium  

if all other markets are in equipment so at  the end all the markets will be in equilibrium

then if individual preferences are convex then  every allocation every point of the contract curve  

that we have shown in this utility frontiers  in this utility possibilities frontier every  

efficient allocation is a competitive equilibrium  for some initial allocation of goods so literally  

this theorem tell us that any equilibrium theme  to be equitable can be achieved by a suitable  

distribution of resources among individuals  and that such a distribution is going to need  

not in itself generate inefficiencies so at the  end unfortunately all programs that redistribute  

income in our society are economically costly  but at the end we want to find efficiency so  

um just to close this this this part of the  chapter we should focus on this point that  

we could find we can find an equilibrium if we  have a competitive market and that day welfare  

sorry the water's low is this economic theory  that tell us that if there is an excess supply  

it could be matched with an excess demand so we  can find out at the end a general equilibrium  

okay and that's all for this  video see you in the next one