(90 points) A firm has the production function q=f(L,K)=KL. (a) (10 points) Find the marginal products of labor and capital. (b) (10 points) Does this firm exhibit diminishing marginal returns to labor in the short run? Show work to explain your answer. (c) (10 points) Derive the marginal rate of technical substitution, MRTS. (d) (10 points) Show whether isoquants are strictly convex. (e) (10 points) Determine the returns to scale for this production function. (f) (10 points) Derive the elasticity of substitution, . (g) (10 points) Find the conditional input demand functions for labor and capital. (h) (10 points) Derive the firm's expansion path. [Your final answer should be an equation, not a picture.] (i) (10 points) Derive the firm's long-run cost curve. [Your final answer should be an equation, not a picture.] (90 points) A firm has the production function q=f(L,K)=KL. (a) (10 points) Find the marginal products of labor and capital. (b) (10 points) Does this firm exhibit diminishing marginal returns to labor in the short run? Show work to explain your answer. (c) (10 points) Derive the marginal rate of technical substitution, MRTS. (d) (10 points) Show whether isoquants are strictly convex. (e) (10 points) Determine the returns to scale for this production function. (f) (10 points) Derive the elasticity of substitution, . (g) (10 points) Find the conditional input demand functions for labor and capital. (h) (10 points) Derive the firm's expansion path. [Your final answer should be an equation, not a picture.] (i) (10 points) Derive the firm's long-run cost curve. [Your final answer should be an equation, not a picture.]