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.)

Interpret data related to R&D expenditures and determine optimal spending levels.

Understand the concept and importance of utility maximization in consumer behavior.

Comprehend the three-step process of technological advancement: invention, innovation, and diffusion.

Analyze how changes in product prices and consumer income affect consumer choices and utility.

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Definitions:

Direct Labor Hours

The number of labor hours spent by workers who are directly involved in the production of goods or services.

Materials Requisitions

Documents used to request the transfer of materials from inventory for production purposes or other internal use.

Job Cost Sheets

Documents that track and record all the costs associated with a specific job or project.

Cost Allocation

Cost Allocation is the process of identifying, aggregating, and assigning costs to cost objects such as products, departments, or projects to accurately represent where expenses are incurred.