Production Functions 1) Consider a production function Y =F (KL), where Y stands for output, K for capital, L for labor. Assume that a firm producing Y with this technology can buy any amount of K and L at constant prices (i.e., the firm is a price taker in the market for K and L). a) Plot a graph with the inputs K and L on the two axes, and draw a so-called isoquant. An isoquant represents all combinations of inputs K and L that will result in the same level of output Y (e.g Y :1 00 could be achieved by using K210 and L210, but also by K:8 and L:13 and numerous other combinations). Hint: usually isoquants are convex shaped. b) Constant returns to scale means that output increases at the same rate as inputs. In particular, doubling all inputs (K and L) will lead to a doubling of output. Increasing returns to scale implies that output would increase by a higher rate than inputs, and decreasing returns to scale means that output increases at a lower rate than inputs. Draw three diagrams, one for each concept (constant, increasing and decreasing returns to scale). In each diagram draw the isoquant from a) representing an output of Y:100. Then draw a second isoquant in each of the three diagrams representing an output of Y:200. The second isoquant represents therefore a doubling of output. Given that each of the three diagrams represents different returns to scale those second isoquants have to differ across them. How do they differ and why? 2) Now consider some specic functional forms. A is a productivity parameter and you can assume A:2. a) Suppose Y=F(K,L) =AK0'7L0'3. Using excel, show it has constant returns to scale. b) Suppose Y:F(K,L) :AK0'7L0'2. Using excel, show it has decreasing returns to scale. c) Suppose Y=F(K,L) =AK0'7L0'4. Using excel, show it has increasing returns to scale. (1) From the point of view of increasing output in each of the above cases, which has a larger impact: doubling K while keeping L constant, or doubling A? Why