#### week 1 - general equilbrium basics and trade

explain the partial equilibrium

utility maximisation shown by demand curveprofit maximisation shown by supply curve - equilibrium: demand=supply- model of market for one good, agents producing a simple good = single good economy

explain broadly why we need the general equilibrium

we have many many products where a price change for one product causes a change in demand and supply for all other products

what assumptions are needed to have market clearance

1. no frictions - no externalities- there are indirect effects but not direct effects- no distortionary taxes - can have lump sum taxes but no distortionary 2. pice taking - no negotiation or market power

set up an edgeworth box with two products and alice and bob when there is no production

- two goods: x1 and x2- two agents: alice and bob- alice and bob have endowments of goods- alice and bob maximise utility subject to the endowment i.e. rational- can trade good between themselves without any distortions and being price takersAlice (ED CUP)endowment: Wa=(wa1, wa2) consumption: Xa=(Xa1,Xa2)Utility: ua(x1,x2)demand: Xa(p1,p2,pwa) -> function of incomeprices: p=(p1,p2)Bob (ED CUP)endowment: Wb=(Wb1, Wb2)consumption: X(Xb1,Xb2)demand: Xb(p1,p2,wpb) -> function of incomeutility: Ub(x1,x2)price: p=(p1,p2)

in order to form an edgeworths box what are alice and bobs problems when there is no production

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draw an edgeworth box

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draw an edgeworth box where demand for good 1 exceeds the endowment of good 1

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draw an edgeworth box where endowment of good 2 exceeds the demand for good 2

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if there was exceess demand for good 1 and excess endowment for good 2 explain and draw how there would be adjustments towards equilibrium

- increase the price of good 1 relative to good 2 , can do this because the actors are price takers - the market clears- competitive equilibrium is reached

state the equation of a competitive equilbrium

(x, p) such that Xa(p*, (p*)*(wa))+xb(p, (p(wa))+xb(ph that Xa(p*, (p*)*(wa))+xb(p*, (p)(wb)=Wa+Wb

what is the general main statement of the competitive equilibrium

suppose that in an exchange economy, consumers preferences are continuous, monotonic and convex, and e>0 then.. competitive equilibrium exists

explain the idea of the proof of the competitive equilibrium

define excess demand for good 1 as z'(p)=(Xa1(p)-Wa) + (Xb1(p)-Wb1) fix p2=1 and vay p1 ( if one market clears, both will clear.. if all but one market clear the last will do if find the point for (n-1) goods the the last one will clear

what is a walrasian equilbrium

competitive equilbrium in exchange economy

how do you exclude the possibility of non existence market clearing e.g. price jumps

clear all but that market and then the walrus law gets rid of the possibility of this (if all but one clears then the last one will)

what are the assumptions of the competitive equilbrium

#NAME?

bob is endowed will all x1 and doesn't want to give any and alice always wants some so a competitive equilbrium can't be reached, draw it and state what assumption is this violating

w>0

set up the production economy

Consumer endowment: a unit of leisure R utility: u(x,R) where R= 1-Lowns the firm and its profitsFirmproduction function: F(L)pay wages w to the consumerproduces good x at price p two markets: labour and good 1

write and draw the consumer problem in the production economy

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write and draw the firm problem in the production economy

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how do you combine the consumer and firms problems in a production economy

here the good is in excess demand : price too low and labour is in excess supply: wage is too high

in the case of the goo being in excess demand and labour in excess supply in the production economy how do you need to adjust prices? and draw it

increase the price of the good relative to the labour MRSa=MRSb= p1/p2

when you adjust prices/wages how do you write relative prices i.e. whats on top and bottom

p1/p2 w/p

what the main general statement for competitive equilbrium in production economy

suppose that in an production economy, consumers demand correspondences and firms' net supply correspondences exist and are continuous, production is irreversible and there is free disposal, then competitive equilbrium exists

what are the assumptions of the production economy competitive equilibrium

#NAME?

what does the competitive equilibrium model leave out

#NAME?

what is a competitive equilibrium

a vector of prices and allocation that clears every market

show how the comp equilibrium model is affected by IRS

none of the points is a comepititve equilibrium - IRS graph looks like like because labour increases towards the y axis

what assumption does IRS break

continuity - optimise at one point then a completely different one

two producers- firms 1 and 2 produce goods 1 and 2 respectively - prices of goods are : p1, p2- labour is the only input L into production functions: y= G(L)- firms make profit pi=pG(L) - wLone consumer- inelastically supplies 1 unit of labour at wage w - consumes goods x1 and x2 and gets utility u(x1,x2)- owns the firm (shareholders not in control)

in the trade model how many markets are there

x1, x2 and labour = 3

explain the trade model and draw it

#NAME?

what are the assumptions of the trade model

- consumer owns the firm - labour only input into production functions - consumer inelastically supplies 1 unit of labour at way w- balance of payments - firms too small to effect price - identical consumer preferences - countries have different production function

what is meant by balance of payments

expenditure on net exports of x1 = expenditure on net exports of x2 volume of imports = volume of exports

whats the autarky budget

consumer expenditure = firms sales = consumer budgetunder autarky production of each good = consumption of each good MRS=MRT=p1/p2

- the ability of country to trade at any world prices other than autarky prices makes the consumers better of- direction of trade is irrelevant for improving consumer's utility - even specialisation is not necessary for improvement (although leads to more gains) - consumers in two autarkic countries will always benefit form trade if consumers within a country are identical

show how specialisation leads to optimal production and gains from exchange leads to suboptimal production

red movement shows gains from exchange x1 produced slightly less and x2 more orange shows specialisation where can see big shift in consumer utilisation

show and explain the trade model where there are two countries and it shows comparative advantage

- two countries in autarky - then have world prices (black line) p1/p2- country 2 produces at red dot so more x2, less x1 - country 1 produces at red dot so more x1 and less x2 country 2 exports x2 and imports x1 - utility is higher

show and explain the trade model where there are tow countries and one has an absolute advantage

1. green line is world prices p1/p2 = MRT 2. can see that country 1 (blue) imports x1 and exports x2

whats an issue with the trade model

#NAME?

set up the multiple industries model i.e. Labour and capital

two producers factors: K and LCost of K is r and cost of L is wGood X is Labour intensiveGood Y is capital intensivefor any wage-rental price ratio, optimal K/L for good Y is higher than for X

what are the assumptions of the multiple industries model

#NAME?

show the graphs for the multiple industries model

#NAME?

explain Rybczynski Theory

#NAME?

what are the assumptions of Rybczynski theory

multiple industries model assumptions- CRS- Competitive markets for labour and capital therefore, zero profits- no unemployment - all capital and labour used - goods prices remain the same

explain Stopper samuelson theorem

1. if relative prices increase (Px/Py) then marginal product of labour increases because the workers have become more valuable as what they are producing is worth more. so then the real wage rises because its within a competitive market so w/r increases2. because the mpl has changed the optimal ratio of K and L changes and gets close to the K axis becuase it is relativey cheaper3. both goods are now produced with relatively more capital and relatively less labour hence, more of good x and less of good y (because price of x has increased - step1)

whats the mpl

price * Q'(L)

what does Stopler - Samuelson Theorem show

if there are constant returns to scaled if both goods continue to be produced, a relative increase in the price of a good will increase the real return to the factor used intensively in that industry and reduce the real return to the other factor

what are the assumptions of stapler - samuelson model

CRSboth goods continue to be produced

explain the redistribution of profits between two firms

1. price of x2 is increased due to removing tariffs and having world prices so profit of firm2 MPL=w shifts up (area under is profit)2. new equilb point to clear labour 3. firm 1 produce less and profits decline. firm 2 produce more and profits increase overall mpl and profit increase

give an example where trade has hurt producers and what was done to prevent it

corn laws -> ireland 1846the corn laws blocked the import of cheap grain by imposing import duties so it was too expensive to import from abroad even when food supplies were short ---> peoples wealth went down but bread makers wealth went up and they were the poor peopled they secured permanent employment

can't decide which would be fairer out of single market or unilateral free tradesingle market- free trade in a very large market, but tariffs with countries outside the single marketunilateral free trade-no incoming trade tariffs with any country in the world but all other countries, including the EU may impose tariffs

what does it mean if allocation x Pareto -dominates allocation x'

if everyone strictly prefers x' to x

what does it mean if an allocation is Pareto - efficient

its not pareto dominatednoone can be made better without making someone worse off weak criterion - not particularly powerful not all outcomes can be Pareto compared says nothing about inequality, only about elimination of free lunch

what is the utility possibility frontier

it describes the utility of agents when we reallocate these resources U={u(y) such that sum of y equals the sum of x aka its like a closed economy vibe}

use Pareto efficiency to redistribute resources

x" does not pareto dominate x and it is pareto efficient to x'but since the sum of x" equals the sum of x' because they're on the asme utility frontier then resources from x" can be feasibly reallocated to achieve x' that pareto dominates x

what are different approaches to deciding the best point on the utility possibility frontier? and what do you need in order to answer this q

you need a social welfare function W(u) i.e. decide how much care about utility of each agent 1. concern for the worst off2. indifferent to inequality: care about total sum3. inequality averse: weight different agents- make sure they don't become too badly off but care more about least favoured person

show graphs and write swf and label to guy who coined it for social welfare function for 1)concerns for the worst off, 2)indifference to inequality and 3) inequality averse

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explain the societal optimisation problem with a W(u) of indifference to inequality and on inequality averse

inequality averse is pareto efficient but not welfare max because care about inequality indifference to inequality is pareto optimum and welfare max fix a resource constraint of the social welfare function then derive the utility possibility frontier U and max welfare W(u) subject to U --> use to see if competitive equilibrium is 'good'

when is general equilibrium needed

if feedbacks of changes are likely to be important e.g. things are sub, complement, inputs in production

whats the main advantage of the system of competitive equilibrium

doesn't need someone in control and neither need to know about the other choice only about their own preferences

explain consumption efficiency and it in the context of edgeworth box

an allocation of commodities such that, given the total supplies of the commodities, the only way to make one person better off is to make another person worse off in edgeworths box - form contract curve - necessary condition for consumption efficiency is MRS1=MRS2

explain production efficiency

an allocation of inputs such that the only way to increase the output of one commodity is to decrease the output of another commodity MRTSchesse=MRTSwinecommodities and inputs in fixed supple

explain production possibility curves

when production efficient , rate at which the economy can transform one output into another by shifting its resources, the negative slope of the production possibilities curve MC1/MC2 =MRT2,1

exilian allocative efficient

MRS1 =MRS2 =MRT2,1