walrus Flashcards
what was the main difference for the theory of exchange of two commodities between walrus and jevons?
the main difference between walrus and jevons was that walrus did not see the need to reduce the population to a limited number of economic agents
what was the main difference for the theory of exchange of two commodities between walrus and menger?
a major difference between walrus and menger was that walrus used continuous mathematical variables rather then mengers simple table of numbers
what is the similiarity between all three marginalists?
in the work of all three authors, the transactions are allocated quantities of the two goods and are left to reallocate their holdings of goods in order to maximise their satisfaction
what was walrus theory of exchange of two commodities?
he assumes that every person is allocated abritarary quantities of the two goods. if the initial allocation is not satisfactory by any person then they can exchange with a person desiring more of a good is the demand and person offering the good is the supply. in a two good world a person dissatisfied must supply one good in order to demand another. assume he is initially given q1 of good 1 so if he offers some good 1 to acquire good 2 the quantity of good 1 left is q1 - o1 where o1 is positive. if he wants to acquire more of good 1 he must offer good 2 so offer of good 1 is negative. he aggregate the single individual to whole community so total amount of goods is Qn. trading does not alter amount of good 1 in circulation so sum of offers is equal to 0. this in other words means supply is equal to demand. the modern approach to utility functions is to treat them as genuine functions of many variables so in a two good world one have: U = f[(q1 -o1),(q2-o2)]. it is possible to assume the utility functions are separable making total utility the sum of the functions: U = f1(q1-o1)+f2(q2-o2). walrus assumed that every person in his system acted with such a utility function attempting to maximise satisfaction. he became first example to derive demand curves from utility functions
what is walrus theory of pure exchange?
he extends the number of transactors and the number of commodities so all goods are included. he aims to show how markets and trade determine equilibrium.
he assumes a world where nobody works so no production, technology or inputs and outputs. the quantities n goods are distributed arbitrarily among population.so individual has Q= q1 +….. qn. if this distribution is not satisfied then the individual can trade. so will have offers o1…..on with some o being positive(supply) and some negative(demand). total utility = f1(q1-o1) +.. fn(qn-on) with all individuals assumed to have same utility function and objective to maximise utility. any increase in quantity increase utility. there is a constraint of not being able to buy any more goods.budget constraint was internally determined that is incomes could be spent result from trading. constraint = o1p1 + …. onpn = 0 where p represents price of goods so offers equal zero. one good is the numeraire with its price set equal to unity so there are n-1 prices to determine. this leads to equation On=Fn(p2,…pn) for whole population. as supply equal demand they are in equilibrium and as there are only n-1 because we know p1=1 then we have a set of simultaneous equations to solve. he claims the equations are sufficient to determine the price and he claims the solution represents workings of competition. the outcome then is that walrus purports to provide a theory of prices that is prior and independent of any notion of costs and production thereby wholly rejecting prior economists whose value theories were founded on production costs.
what was tatonnemnet?
it was a trial and error process in which a price is announced, effectively by some hidden auctioneer and demanders and suppliers responded to the price. if there were an excess supply demand then the price would be fall and vice versa and thus would the prices move toward the equilibrium. walrus says the task was to show that the upward and downward movements of price solve the system of equations for offer and demand by a process of groping.
equilibrium is arrived at in the market by raising the price of those commodities the demand for which is greater than the offer and by lowering the price of those commodities the offer of which is greater than demand
how does walrus introduce production into his theory?
in part 4 walrus intoduced production however the inputs themselves are not produced. this does not matter for labour and land but for capital goods walrus can not properly introduce. walrus assumes that these endowment goods also have a direct utility for each individual. so individual can either retain them or hire them out. assume n consumption goods produced. assume that there are m non produced inputs which used in production of consumption goods. assume a particular individual possesses an endowment of these input goods. a1….am. these goods can then be traded if not suitable to individual so (a1-o1)…(am-om) . consumption goods have to be produced. the budget constraint changes which is now the amount any transactor can spend on consumption goods must come from income derived selling the services of input goods. so the individual aims to maximise the utility function U=f[q1…qn , (a1-o1)….(am-om) where q is quantity of consumer goods and am-om is the differences between original endowment of input goods and final amount retained after trade. budget constraint is now equal to the income obtained from the productive hire of offers so q1p1+..qnpn =o1V1+….onVn where p is price of consumption goods and V is price of inputs. walras assumes fixed input coefficients for the production of the consumption goods, that is, there is only a single method of producing any good.
what is the demand fucnction for goods for walrus under production?
if we sum over all indiviudal demand functions, the demand for a good one can be written as Q1 = F1(p1,….pn, V1,…..Vn)
what is the supply fucntion for goods for walrus under production?
summing up all the individual there will be a set of supply funcitonf of productive inputs. these will be functions of all the prices,
O1= F1(p1,……pn ,V1….V m )
what is missing in walras wor?
it is clear that capital must themselves be produced, they will wear out or depreciate and must be replaced from new output. new methods of production and invented requiring the production of new capital goods. moreover as there was no capital stock , there was no profit on capital so part 4 had an absence of the proper rate of profit.
what were the extensions to walrus work?
in part v he introduces capital goods proper, goods that wear out or depreciate and must therefore be produced, as more goods produced, more technologies must be specified to give the inputs needed to produce outputs of capital goods. additional equations are needed to give the prices of both consumption and capital goods and prices now must include a rate of profit.
