Question

Jake and Paul run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant’s long-run production function is q = 4 K0.75 L0.25, where q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 10K + 2L, where C is the total weekly cost.

a. (2 points) Given the production function in this problem, use calculus to derive the marginal products of labor and capital.

b. (2 points) Making use of your answer to a, what is the ratio of capital to labor minimizes Jake and Paul’s total costs?

c. (2 points) Making use of your answer in b, how much capital and labor will Jake and Paul need to rent and hire in order to produce 1,000 reams of paper each week?

d. (1 point) How much will hiring these inputs cost them?

e. (4 points) Use a Lagrangian to solve the constrained cost-minimization problem for the producer to confirm your answer to part c.

f. (1 point) What is Jake and Paul’s expansion path?

g. (4 points) What is Jake and Paul’s reduced form demand for capital?

h. (1 point) Use calculus to confirm that the demand for capital satisfies the Law of Demand.

Answer 1

Note: Post four subparts at a time.