Homework Help: Economics (Production Possibility Frontiers)

Posted by Susan on Sunday, December 6, 2009 at 4:28am.

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?

Solution:
A straight line from (X=20, Y=0) to (X=0, Y=40).

Explanation:
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.

Economics (Production Possibility Frontiers) - economyst, Monday, December 7, 2009 at 1:13pm
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).

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