4. Assume that the aggregate production function for an economy is described by:

Question

4. Assume that the aggregate production function for an economy is described by: where 0 < < 1. a. Show the production function has the property of constant returns to scale. b. Obtain the per capita production function (Hint: Divide the above production function by L, and express all variables in per capita terms; e.g. y = Y/L, k = K/L using lowercase letters to denote per capita variables). c. Draw the per capita production function with k on the horizontal axis and y on the vertical axis. Is it concave downward? Why?

Explanation / Answer

4) Constant returns to scale means if the factors like labour and capital will increase by n times then output will also increase by n times. So multiply each factor by n and put it in production function and if output of new production function can be represented by n XQ form then it follows CRS.

For calculating per capita functions we need production function which is not mention here.

Percapita production functions are concave downward sloping because it shows with increase in factors productivity decreases since there is scarecity of other factor in the process and all the factors are not perfectly substitute.

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