Question

A basket of goods for a given consumer includes two​ goods, X and Z. Consumer income is equal to ​$1,500 and the prices of these two goods are as​ follows: Px​ = ​$50 Pz​ = ​$50 This consumer is consuming 10 units of good X. Suppose that over the course of a​ year, the price of good X changes by -20​% and the price of good Z changes by 25​%.

How much income would be required for the consumer to afford the same quantity of goods X and Z with the new​ prices?
What is the rate of inflation?
Given this change in prices, is it possible for our consumer to buy the original bundle of goods?

Answer 1

Costumer will need $1650 to afford the same quantity of goods

Rate of inflation=2.5%

Is not possible for our consumer to buy the original bundle of goods

Step-by-step explanation:

Income = ​$1,500

First year Px​ = ​$50

Pz​ = ​$50

10 units of good X is 50x10=500,

Consumer could buy $1000 in product Z (Income-cost of product Z=1500-500)

qz=Product Z is $50 each so customer could buy 20 units(1000/50).

Prices of Second year

Px'​ = ​$50*(1-0.20)=40

Pz'​ = ​$50*(1+0.25)=62.5

Cost=Px'*qx+Pz'*qz=40*10+62.5*20=400+1250=1650

Costumer will need $1650 to afford the same quantity of goods

Rate of inflation=

RI=(sum price of x and z in second year-sum price of x and z in first year)/100

RI=(40+62.5)-(50+50)/100=102.5-100/100= 2.5/100=0.025=

RI=2.5%

Is not possible for our consumer to buy the original bundle of goods with the same budget