4. Consider the following production functions: (i) Q = 4K2L2 (ii) Q = 2K + 4L...

4. Consider the following production functions: (i) Q = 4K2L2 (ii) Q = 2K + 4L (iii) Q = min(4K, 5L)

a. Graph an isoquant for Q = 400 for each of the production functions above.

b. In few words, explain what does the MRTS tell us about a production function?

c. Find the MRTS for production functions (i) and (ii).

d. Find the MRTS for production function (iii)

Expert Solution

b) MRTS can be defined as amount of capital input that has to be given up to use an additional unit of labor so that output remains constant. MRTS is measured by the ratio of marginal product of labor and marginal product of capital.
Q = 4K² L² ( In this case production function is cobb douglus and iso-quant will be convex to orgin. This is due to dimnishing MRTS. )
Q = 2K + 4L ( In this case labour and capital are perfect substitutes which means inputs can be exchanged at a constant rate then Iso-quant will be a straight line. This is because MRTS will remain constant.
Q = min(4K, 5L) ( In this case labor and capital are perfect complements then iso-quant will be L-shaped. Inputs will be called perfect complement when both inputs must be used together in a fixed proportion.MRTS will be 0 or infinity because marginal product of each input will be zero.

Rahul Sunny answered 9 months ago

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