Consider the production function q = f(L,K) = ALªK®, where A, a, b are positive constants. For what values of A, a, and b are there diminishing marginal returns to labor L? What about diminishing marginal returns to capital? b. For what values of A, a, and b does the production process have diminishing marginal rate of technical a. substitution? c. For what values of A, a, and b are there constant/decreasing/increasing returns to scale?

A Firm's Optimization with CES Production Function The Constant Elasticity of Substitution (CES) production function is a flexible way to describe how a firm combines capital and labor to produce output, allowing for different levels of substitutability between the two inputs. The elasticity of substitution, denoted by σ, measures how easily the firm can substitute capital for labor (or vice versa) while maintaining the same output level. The parameter p is related to the elasticity of substitution by the formula σ = 1/(1 - p). Now, let's consider a firm that operates for two periods (t and t + 1) and produces output according to the CES production function: F(Kt, Nt) = [aK{ + (1 − a)N]¹º 0