Question

1. Consider the production possibility frontier for a simple two-good (closed) economy. Quantities of good x produced are plotted on the horizontal axis. Quantities of good y produced are plotted on the vertical axis. Suppose that the production of both x and y depends only on labor input and that the production functions for these goods are: x = f(l_x) = l_x and y = f(ly) = l_y. Total labor supply is limited by: l_x + l_y = 100. The typical individual’s utility function is given by U(x,y) = x·y. The equilibrium price ratio p_x*/p_y* is equal to [r]. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed. HINTS: First derive the production possibility frontier equation.)

Answer 1

Production possibility curve is the curve that depicts the combination of the amount of good X and good Y that can be produced given the available inputs in the economy.

x = f(l_x) = l_x

y = f(ly) = l_y

l_x + l_y = 100 .... (1)

The amount of good X produced = the units of labor used to produce good X. The maximum amount of good X that the economy can produce is when all the labor is employed in the production of good X, that is 100 units. The maximum amount of good Y that the economy can produce is when all the labor is employed in the production of good Y, that is 100 units.

Put the value of X and Y in equation 1.PPC is linear with intercept being 100 and slope being -1.

X+Y = 100

Y = 100-X

At equilibrium, slope of IC = slope of PPC

Y/X = 1

Y = X

Therefore, equal amount of both the goods are produced. The equilibrium price ratio p_x*/p_y* is equal to 1 (slope of PPC).