Question

A consumer has #300 to spend on goods X and Y. The market prices of these two goods are Px = #15 and Py = #5. 

a. What is the market rate of substitution between goods X and Y? 

b. Illustrate the consumers opportunity set in a carefully labelled diagram. c. Show how the consumers opportunity set changes if income increases by #300. How does the #300 increase in income alter the market rate of substitution between goods X and Y?

Answer 1

Total money with consumer = #300

Price of Px = #15

Price of Py = #5

a)

market rate of substitution between goods X and Y

$=\frac{Px}{Py}\\=\frac{15}{5}\\=3\space units$

b)

With given income, the quantity of Y and X purchased:

Quantity of Y$=\frac{300}{5}=600\space units$

Quantity of X$=\frac{300}{15}=20\space units$

c)

If income increase by $300. So, the new income is $600.

Quantity of Y$=\frac{600}{5}=120\space units$

Quantity of X$=\frac{600}{15}=40\space units$

The market rate of substitution will not change because there is an increase in income and the market rate of substitution depends on the price of the commodity.