Question

Exercise 5
Suppose bread and jam are perfect complements, ie they are always used in a one-to-one ratio and in
form of bread slices and jam portions. These are the only items that consumers buy.
a) Explain why the demand for bread (x1) and the demand for jam (x2) can
is expressed in the form
??1 = ??
??1 + ??2
and ??2 = ??
??1 + ??2
where Y is the income, while p1 and p2 are the price of bread and jam respectively.
b) Explain, and preferably also analytically, that if the price of bread is equal to the price of jam, so is
the price elasticity of bread demand (the elasticity of x1 with respect to p1) equals –1/2.
c) What are the cross-price elasticities (the elasticities of x1 with respect to p2, and x2 with respect to
on p1)? Explain

Answer 1

Exercise is We have i Demand x Demand n for bread a for jam. pe price of bread of " Pe price of jam. y Income a.) In case of perfect complements we treat both the - goods together as a single good, since consumption i of one does not take place without the other. That is why the prices of these two goods are added and the aggregate price is treated as the price of the single good.

Here, bread and jam are perfect complements, i.e, they are always used in a one-to-one ratio. This implies that the number of bread slices is equal to the prope portion of jam, i.e, both of their demands are equal and heme, we can say that m=x₂ = n(say). In the following diagram we have considered the indifference wines relevant in this case "Jam (222) - I 3.0, J.CZ .Ci K K J - > Bread (au) - In the above diagram, I.4 and I. Ca are two 'L' shased is isoquants, and it we wone along the OA ray, we will get more of these Ľ shaped IC's . The budget constraint in this case would be: Y = pisut P2R2 . =) Y = P1 x + P2 x (sine, %4= xy = x) un Y Þi + P2 Therefore, we = 22 (pr+P2)

D. Further, we have that i Pi = P2 = Þ (say) Therefore, the demand for 4 (or dy or x) becomes : 25 of the boy por => x = (since, pr= 2). Therefore, d . 2 p I change Now, we know that elasticity measures the change in quantity demanded of a good in response to : change in it's price. It is given by : Eon = dumu, Zsoi api/B Where, Essi is the price elasticity of demand for ti daulu, kad • ES DI = i Esai does api 25i2 bi >> Espi=-1. Again, if we consider us, we have - (sime, u = xq and pi=P2). n = 262

Esp2 - das P2 weD2 dp2ren 5- 2pg3 2 Þ2 = - 1, where we is the price Fruity of demand 'for good 2. Hence, we have: Es = Eusn =-1, where the a sign indicates the inverse relationship between price and quantity of the good. ©). Cross price elasticity is the measure which tells - us how the quantity demanded of a good changes în response to changes in the price of related geod (in this case la complementary good). We can write: = Y (sime, p1=p2) 252 or nye vy (since pe=pa). 2PI Nu Hewe, .. 8 2 Elasticity of sy = with tespeet topi A 2

ngain, aga iNang i plasticity of ng with respect to p2, E3D21: . PL YD2 021 = dpi = Y . Ppia the = -1 i EsDi2 = E9D21=-1. Here, the cross-price elasticities are similar to own price elasticities. Intuitively, this is because the goods are complements and changes in price of any one good affects for the demand for both the goods equally.