Variant 4. The PPF of the country can be described by the equation y=sqrt (128-x^2)(xgeqslant 0 ygeqslant 0) . The country enters the world trade where prices are p_(x)=2,p_(y)=2 1. Derive the TPF equation. 2. Calculate the opportunity cost of producing x in the point x=5

1. To derive the TPF (Terms of Trade) equation, we need to find the ratio of the price of good x to the price of good y. Given that the prices are and , the TPF equation is simply the ratio of these prices, which is .2. The opportunity cost of producing x in the point can be calculated by finding the amount of good y that must be given up to produce an additional unit of good x. This can be done by taking the derivative of the PPF equation with respect to x and evaluating it at .The derivative of the PPF equation with respect to x is: at gives: Therefore, the opportunity cost of producing x in the point is .