Answer to Question #175430 in Macroeconomics for Osei Kuffour

Question

1. An individual spends all his income on three goods. He buys 550 units of X at $1 per unit, 425 units of Y at $2 per unit and 200 units of Z at $ 3 per unit. The price of X increases by 10%, but there is no change in prices of Y and Z. He now buys 440 units of Y and 190 units of Z. Calculate his price elasticity of demand for X. An individual spends all his income on three goods. He buys 550 units of X at $1 per unit, 425 units of Y at $2 per unit and 200 units of Z at $ 3 per unit. The price of X increases by 10%, but there is no change in prices of Y and Z. He now buys 440 units of Y and 190 units of Z. Calculate his price elasticity of demand for X.

  

Answer 1

Money Spent on Buying X = 550 x $1 = $550

Money Spent on Buying Y = 425 X $2 = $850

Money Spent on Buying Z = 200 X $3 = $600

Through above data the Income of an individual can be calculated by adding all three values because he spends all his income on these three goods = $550+$850+$600 = $ 2000

In second condition Price of X is increase by 10% and price of other item is same.

so,

Money Spent on Buying Y = 440 X $2 = $880

Money Spent on Buying Z = 190 X $3 = $570

Money Spent on Buying X = $2000 - ($880 + $570) = $550

As the price of X increased by 10%. So the new price will be $1.1.

New quantity purchased of X = $550 divided by $1.1

= 500 Units

Now lets calculate Price elasticity of demand for X:

Price elasticity of demand for X = % change in quantity demanded $/$ % Change in Price

= $\frac{(Q2 - Q1)}{Q1)}\div \frac{( P2-P1)}{P1}=$ $\frac{(500 - 550)}{550}\div$$\frac{(1.1 -1)}{1}$

= - .909

=|-0.909|=0.909