1 Production in the long and short run

a. Demonstrate that returns to scale are constant.

b. Derive the marginal products MP1 and MP2 and discuss how they depend on levels of inputs. Demonstrate that the equality holds.

b. Derive the marginal rate of technical substitution MRTS12 and explain that the isoquants are decreasing and convex.

c. Suppose that the amount of input 2 is fixed, i.e. Explain that economies of scale of the short-run production function are decreasing.