The Edgeworth box diagram can also be used to show how a production possibility frontier is constructed for an economy as a whole. Suppose there are only two goods that might be produced (X and Y), each using two inputs, capital (K) and labor (L). In order to construct the X-Y production possibility frontier, we must look for efficient allocations of the total capital and labor available.

a. Draw an Edgeworth box with dimensions given by the total quantities of capital and labor available (see Figure).

b. Consider the lower-left corner of the box to be the origin for the isoquant map for good X. Draw a few of the X isoquants.
c. Now consider the upper-right corner of the box to be the origin for the isoquant map for good Y. Draw a few Y is oquants (as in Figure) in the Edge worth box.

d. What are the efficient points in the box you have drawn? What condition must hold for a given allocation of K and L to be efficient?
e. The production possibility frontier for X and Y consists of all the efficient allocations in the Edgeworth box. Explain why this is so. Also explain why inefficient points in the box would be inside the production possibility frontier.
f. Use the connection between your box diagram and the production possibility frontier to discuss what the frontier would look like in the following cases:
i. Production of good X uses only labor, production of good Y uses only capital.
ii. Both X and Y are produced using K and L in the same fixed proportions as the inputs are available in the economy and both exhibit constant returns to scale.
iii. Both X and Y have the same production function and both exhibit constant returns to scale.
iv. Both X and Y are produced using the same production function and both exhibit increasing returns toscale.

Transcribed Image Text:

Output of Y per week slope 3 X =Y 0 10 V50 X = 2Y 120 slope =-1 1 11\Slope =-2 、'10 .50 t10 Output of X per week io 220 O, Total Os -Total X