Economics (Production Possibility Frontiers)
posted by Susan .
Assume that the endownment of capital and labor in a given society is 20 units of capital and 20 units of labor. The production function of good X can be expressed as X = K1/2L1/2, and the production of good Y can be expressed as Y = K + L. Which of the following describes society's production possibility frontier?
A straight line from (X=20, Y=0) to (X=0, Y=40).
If society devotes all resources to making X, X = 20. If society devotes all resources to making Y, Y = 40. The production possibility frontier is a straight line because there are constant returns to scale for both goods.
I think it is line from (X=8.94, Y=0 to (X=0, Y=40). The line will be in a bow-shape.
(I presume by: X = K1/2L1/2 means K and L are raised to the 1/2 power.)
To see this, plot a graph. (Excel spreadsheets would be very helpful here).