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​ = ​$25 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 −10​% and the price of good Z changes by 10​%. 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?

Answer 1

Income = $1,500

Px = $25

Pz = $50

Consumer is consuming 10 units of Good X. Expenditure on good X is $25 * 10 = $250. Thus, expenditure on good Z is 1,250 which means (1,250 / 50) = 25 units of Z are consumed

If price of X reduces by 10% such that new price of X is $22.5 and price of good Z rises by 10% such that new price of Z is $55

If consumer still consume 10 units of good X and 25 units of Z are consumed, total expenditure would be $22.5 * 10 + $55 * 25 = $1,600

You would need $100 more to consume the same bundle. Inflation rate = [(1,600 - 1,500) / 1,500] * 100 = 6.67%