Fixed Input Relations

question 14

Essay

Fixed Input Relations. Extreme Biking, Inc., assembles high-end extreme mountain bicycles at a plant in Lexington, Massachusetts. The plant uses labor (L) and capital (K) in an assembly line process to produce output (Q) where:

A. Calculate how many units of output can be produced with 25 units of labor and 400 units of capital, and with 225 units of labor and 3,600 units of capital. Are returns to scale increasing, constant, or diminishing?
B. Calculate the change in the marginal product of labor as labor grows from 25 to 36 units, holding capital constant at 400 units. Similarly, calculate the change in the marginal product of capital as capital grows from 400 to 625 units, holding labor constant at 25 units. Are returns to each factor increasing, constant, or diminishing?
C. Assume now and throughout the remainder of the problem that labor and capital must be combined in the ratio 25L:400K. How much output could be produced if the company faces a constraint of L = 25,000 and K = 500,000 during the coming production period?
D. What are the marginal products of each factor under the conditions described in part C?

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Definitions:

Activity-Based Costing

A costing methodology that assigns overhead and indirect costs to specific products or services based on the activities that contribute to these costs.

Overhead

The indirect costs of running a business that cannot be directly linked to a specific product or service, such as utilities, rent, and administrative expenses.

Activity Rate

The predetermined overhead rate used in activity-based costing to assign overhead costs to products or services based on a specific activity.

Machine Setups

The process and associated costs of configuring machinery to produce a specific product or batch of products.