Consider the Objective Function $Y=A \times L^{\alpha} \times K^{\beta}$

question 23

Essay

Consider the objective function,
$Y=A \times L^{\alpha} \times K^{\beta}$
where,
Y = total output
A= total-factor productivity
L = labor input
K= capital input
α = capital input share of contribution for L
β = capital input share of contribution for K
a. Assume α = 0.33, β = 0.67, A = 10 and each unit of labor costs $45 and each unit of capital costs $55. With $50,000 available in the budget, develop an optimization model to determine the number of units of capital and labor required in order to maximize output.
b. Find the optimal solution to the model you formulated in part a. Round all your answers to two decimal places. (Hint: When using Excel Solver, use the Multistart option with bounds 0 ≤ L ≤ 700 and 0 ≤ K ≤ 1000.)

---

Definitions:

Net Capital Spending

The total spending on new capital assets minus the sales of disposed or obsolete assets.

OCF

Operating Cash Flow, which represents the cash generated by a company's normal business operations.

Net Working Capital

The gap between a firm's short-term assets and liabilities, reflecting its immediate financial condition.

Cash Flow

The all-encompassing total of fund transactions in and out of a business, essentially shaping its liquid financial state.