Please open the word file to view the mathematical notations.
Consider a firm with production function .
(a) Sketch the isoquant diagram of this firm.
(b) Derive the marginal rate of technical substitution between the two inputs. What is the relationship between the marginal rate of technical substitution and the isoquants drawn in subquestion (a).
(c) Does the function exhibit decreasing, constant, or increasing returns to scale? Is homogeneous of some degree k>0?
(d) Write down the firm's cost minimization problem.