The Longheel Press Produces Memo Pads in Its Local Shop

question 146

Essay

The Longheel Press produces memo pads in its local shop. The company can rent its equipment and hire workers at competitive rates. Equipment needed for this operation can be rented at $52 per hour, and labor can be hired at $12 per worker hour. The company has allocated $150,000 for the initial run of memo pads. The production function using available technology can be expressed as:
Q = 0.25K^0.25L^0.75,
where Q represents memo pads (boxes per hour), K denotes capital input (units per hour), and L denotes labor input (units of worker time per hour). The marginal products of labor and capital are as follows:
MP_L = (0.75)(0.25)K^0.25L^-0.25
MP_K = (0.25)(0.25)K^-0.75L^0.75
a. Construct the isocost equation.
b. Determine the appropriate input mix to get the greatest output for an outlay of $150,000 for a production run of memo pads. Also, compute the level of output.
c. Explain what would happen in the short run (keeping capital fixed) to the appropriate input mix if production were changed to 1,500 units per hour. Would the input combination be different in the long run? If so, how would it change? Explain.

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Definitions:

Franchise

A system in which entrepreneurs purchase the rights to open and run a business from a larger corporation.

Personal Brand

The unique combination of skills, experiences, and personality that one actively communicates to the world, particularly in professional contexts.

Independence

The state or quality of being self-reliant and free from outside control or not depending on another's authority, support, or resources.

New Career

The beginning or pursuit of a different job path or professional direction.