slope of the production possibility frontier x2+100y2=500

Question

it is related to for an economy that produces public good(y)and private good (x)

Answer 1

PPF is shown in the above graph: x^2+100y^2=500.

The quantity of good x is the horizontal axis and the quantity of good y is the vertical axis.

The slope at any point on the PPF is given by x/100y.

If we take two examples x=10 and x=20 the slope at these points is 10/200=1/20 and 20/100=1/5 respectively. In other words, at the point where the quantity of good x is 10 and 20 respectively. At around x=22 the quantity of x is almost at its maximum potential.

This means that the tradeoff between good x and good y is the decrease in production of y by one unit allowing the increase of x by 20 units in the first case; and in the second case, the tradeoff of one unit of y allows the increase of 5 units of x, where x is realising its maximum potential.