Question

Suppose that the demand and supply function for ice cream are QdI = 85−4PI +6PP and QsI = 5PI − 5, respectively. Suppose the demand and supply function for pie are QdP = 110 − 5PP + 2PI and QsP = 3PP − 10, respectively. (a) Are pie and ice cream substitutes or complements? (b) Solve for and graph the market-clearing curves for pie and ice cream. (c) Find the general equilibrium prices and levels of consumption of both goods.

Answer 1

a)

QdI = 85−4PI +6PP and QsI = 5PI − 5

From the demand curve, we can infer that an increase in the price of pie leads to an increase in the demand for Ice-cream.

QdP = 110 − 5PP + 2PI and QsP = 3PP − 10

Above demand curve shows that, an increase in the price of icecream increases the demand for Pie.

So, both Pie and Ice-cream are substitutes of each other

b) and c)

In market of Ice-cream, equilibrium occurs at QdI = QsI

85−4PI +6PP = 5PI − 5

In market of Pie, equilibrium occurs at QdP = QsP

110 − 5PP + 2PI = 3PP − 10

120 + 2PI = 8PP

PP = (120 + 2PI) / 8

Put value of PP in equation 1

85−4PI +6PP = 5PI − 5

90 + 6*((120 + 2PI) / 8 ) = 9PI

PI = 24

and PP = (120 + 2PI) / 8

= (120 + 2*24) / 8

PP = 21

QDI = 85−4PI +6PP

= 85 - 4*24 + 6*21

QI = 115

QdP = 110 − 5PP + 2PI

= 110 - 5*21 + 2*24

= 53

General equilibrium prices: (PI, PP) = (24, 21)

Equilibrium Consumption: (QI, QdP) = (115, 53)