Question

A consumer has P3,000 to spend on goods x and y. The market prices of these two goods are Px = P150 and 3y = P50.

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

b. Illustrate the consumer's opportunity set in a carefully labeled diagram.

c. Show how the consumer's opportunity set changes if income increases by P3,000.

Answer 1

$\text{a.}\, \text{MRS}=\dfrac{P_x}{P_y}\\ \text{MRS}=\dfrac{150}{50}\\ \text{MRS}=3\\ \text{b.}\, \\ Y=P_XX+P_YY\\ 3,000=150X+50Y\\ \text{when X=0,}\\ 3,000=150(0)+50Y\\ 3,000=50Y\\ Y=60\ units.\\ \text{when Y=0,}\\ 3,000=150X+50(0)\\ 3,000=150X\\ X=20\ units.\\$

In the above graph, if the consumer spends all his income in good y, he would consume 60 units of y and 0 unit of x. And if he spends his entire income on good x, he would consume 20 units of good x and 0 unit of good y. The MRS shows that for every one unit of why consumed given his income, the consumer would be giving up 3 units of good x.

$\text{c. new income=3,000+3,000}\\ =6,000\\ Y=P_XX+P_YY\\ 6,000=150X+50Y\\ \text{when X=0,}\\ 6000=150(0)+50Y\\ 6,000=50Y\\ Y=120\ units.\\ \text{when Y=0,}\\ 6,000=150X+50(0)\\ 6,000=150X\\ X=40\ units.\\ \text{as the consumer's income doubles,}\\ \text{the consumption bundle of the consumer doubles.}$