ECONOM .f2015.pracprob2. Intermediate Microeconomics Economics 4351/7351 Fall 2015 Answers for Practice Problem Set 2, Chapters 6-8

Chapter 6 8. Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of each individual factor as the factor is increased, and the other factor is held constant? a. q = 3L + 2K This function exhibits constant returns to scale. When the inputs are doubled, output will double. Show this explicitly by substituting 2L for L and 2K for K. Then demonstrate the analogous result for any multiple  1and positive. Each marginal product is constant for this total product function. When L increases by 1, q will increase by 3. When K increases by 1, q will increase by 2. b. q =(2L + 2K) 2 1 This function exhibits decreasing returns to scale. When the inputs are doubled, output will less than double. Demonstrate this explicitly. Then demonstrate with positive  1 . The marginal product of each input is decreasing. This can be determined using calculus by differentiating the production function with respect to either input, while holding the other input constant. For example, the marginal product of labor is 1 2 2(2 2 ) 2 L K q L    