Question

3. Suppose an economy has a production possibility frontier characterized by the equation x2+4Y2 100 a. In order to sketch this equation, first compute its intercepts. What is the value b. Calculate three additional points along this production possibility frontier. c. Is the opportunity cost of X in terms of Y constant in this economy, or does it d. How would you calculate the opportunity cost of X in terms of Y in this of Xif Y-0? What is the value of Yif X-0? Graph the frontier and show that it has a general elliptical shape depend on the levels of output being produced? Explain. economy? Give an example of this computation.

Answer 1

a) The production possibility frontier (PPF) of an economy is given as x^2 + 4y^2 = 100 set x = 0 in (1) (0)^2 + 4y^2 = 100 4y^2 = 100 y = squareroot 100/4 y = 5 Thus at x = 0, y = 5 set y = 0 in (1) x^2 = 4 (0)^2 = 100 x^2 = 100 x = squareroot 100 x = 10 Thus at y = 0, x = 10 (b) set x = 3 in (1) (3)^2 + 4y^2 = 100 9 + 4y^2 = 100 y = squareroot 91/4 y = 4.17 set x = 6 in (1) (6)^2 + 4y^2 = 100 36 + 4y^2 = 100 y = squareroot 64/4 y = 4 set x = 3 in (1) (8)^2 + 4y^2 = 100 64 + 4y^2 = 100 y = squareroot 36/4 y = 3 \r\n The following table summarizes the values of y has different values of x