Demand With endowments
Econ 2GG3 (Ed. July 10 2011)h
(Most of this material is based on Varian Ch. 9. & E.E.A
• In the previous discussions we treated income and prices as
exogenous-determined outside the model. We now consider
an alternative set exogenous variables as prices and
endowments. We will use this in the intertemporal model
also use this in studying the labor/leisure choice.
• Consider the case where the consumer is endowed with x*
and y* units of the two goods. If x and y on other hand
represent the consumers gross demands (amount the
consumer ends up consuming) then it must be the case the
value of purchases must be equal to the value of goods she is
i.e xP x yP =yx*P + yxP y This can be rewritten as:
y = (1/P )y x P + x P - xP y and dx/dx = -P /P x y
Here, x P + y x acts juyt like income (say, M*)
More of either endowment (x*P or y*P ) xhifts theyconstraint
outward and parallel.
• The endowment bundle is always on the budget line. The
slope however as before only depends on the price ratio. Note
too that a 10% increase in the price of x cannot be
distinguished from a 10% decrease in the price of y since they
pivot through the same point (the endowment point).
We can rewrite the income constraint as:
x*P -xP = yx -y*P y y
Or (x*-x)P =(x-y*)P y
Here the equation can be thought of as
Sales of x = Purchases of y • This therefore represents the BL expressed in terms of net
demands. The difference between what the consumer ends up
with (gross demand) and the initial endowment. If (x-x* )> 0
then she is a net buyer/demander otherwise if less than 0 the
net seller orsupplier i.e. (x*-x)>0. Consumers less x that her
endowment. Income and substitution effects.
• In analyzing these effects it is important to consider the case
where a consumer is a net seller or a net buyer. Consider the
case where the consumer is a net seller of x and its price
increases. The substitution effect as before is to decrease
consumption of x whose price has risen.
• But since price of x has risen it expands his budget set
(endowment effect)-because he is a net seller of the good
whose relative price has risen. The income effect is therefore
to increase its consumption. These effects therefore oppose
each other even though x is a normal good. We can show that
for a net seller if the price of what she sells goes up, she will
not switch to being a net buyer. (To be shown in class).
• How about in the case where the individual is a net buyer?
The substitution effect is still negative. The budget set shrinks if you are a net buyer of the good whose price has risen and
therefore if the good is normal the income effect is negative
too. We can however show that if the consumer is a net buyer
and the price of what she buys decreases she is better off
remaining a net buyer.
The endowment problem-Finding demands
To solve for the optimal x and y one must solve the following
1. M*=x*P + y*P =xP + yP
x y x y
2. MRS=P /P x y
We have used M* as a shorthand. M* is exogenous and the
x=x (P ,x ,y*)
y=y(P ,x My,
Note however that now when P changes it has both a direct
x effect on x and also an indirect effect through M*
Find the demands associated with U=xy given