What is the price-consumption curve for perfect substitutes ?

Question

What is the price consumption curve of good Y if income is $24/wk, price good X is $3/lb and Y and X are one-to-one perfect substitutes ?

Answer 1

The PCC curve for Y will run from infinity from the top of the Y axis to the quantity of 8y ($3/lb or unit) then on a diagonal across to 8x quantity ($3/lb of x) then out to infinity along the x axis.

The reason for this. PCC of Y is a plot of how much Y and X the person will buy as the price of y increases (and therefore on our X Y graph, as the quantity of y decreases) as X remains the same.
Because they are perfect substitutes when a lb of y costs less than a pound x they will buy all y. This is because the utility they get for y and x is the same (perfect substitutes) and since the price of y is less they maximize utility by buying all Y.

When the price of y is the same as the price of x they are indifferent to the amount of y or x that they buy. For the same budget amount, any combination of x and y will give them the same utility. Therefore the PCC follows this budget line from 8y to 8x.

Then when the price of x is less than the price of y, they will only choose to buy x to maximize their utility. Thus, the amount of y comsumed when the price of y exceeds $3 will be zero up to infinity.

Peace

Answer 2

the curves will be equal if they are perfect subs