Nia’s Pizas is a takeout-only pirm parlor servicing the college campus of Tallahassee that specializes in vegan pirras. Nia’s small shop has barely enough room for customers to stand and wait, let alone the four pizza ovens necessary to keep up with the hungry student custertiers. Nia signed a lease renting both the four ovens and the storefront for the next year. Due to the terms of the lease and the buiding’s site constraint, Nia is unable to change the store’s number of pizza ovens in the shert run. However, Nia does face a decision regarding the number of employees to schedule on a weekly basis. Every Sunday, Nia contacts the staff to communicate the amount of workers needed on each day of the upcoming week. In the stiort run, the store employees are piza ovens are inputs. The following table presents Na’s daily production schedule. ale on a weekly basis. Every Sunday, Nia contacts the staff to In the short run, the store employees are inputs, and FII in the blanks to complete the Marginal Product of Labor column for each worker. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. Hint: Be sure to plot the first point at (0,0). Suppose that Nia’s only variable cost is labor. Assume that Nia faces dally fixed costs of $20 and pays all workers the same daily wage of $30. Use the orange points (square symbol) to piot Na’s total cost curve on the following graph using the quantities from the preceding table. True or False: The shape of the production function reflects the law of increasing marginal returns. True Faise
The Correct Answer and Explanation is :
The law of increasing marginal returns states that as additional units of a variable input (like labor) are added to a fixed input (like ovens), the marginal product of labor initially increases due to better utilization of the fixed resources. However, after a certain point, adding more workers leads to diminishing returns because the fixed input becomes a bottleneck.
To determine whether the production function follows the law of increasing marginal returns, we need to calculate the Marginal Product of Labor (MPL) using the formula:
[
MPL = \frac{\text{Change in Output (Q)}}{\text{Change in Labor (L)}}
]
If the MPL increases for the first few workers before decreasing, then the production function follows the law of increasing marginal returns.
Let’s analyze the concept further:
- Increasing Marginal Returns Stage: At low levels of labor, adding more workers allows better specialization and coordination, increasing productivity. For example, if one worker struggles to manage all tasks, a second worker can specialize in preparing ingredients while the first bakes the pizzas, leading to a higher MPL.
- Diminishing Marginal Returns Stage: Eventually, as more workers are added, they start getting in each other’s way due to space constraints in the small shop. Since the four ovens are fixed, adding too many workers means each has less time using an oven efficiently, leading to a decrease in MPL.
- Negative Marginal Returns Stage (Possible in Extreme Cases): If the shop is overcrowded with too many workers, total output may decline due to inefficiencies, making MPL negative.
Answer: True
The production function does reflect the law of increasing marginal returns at first. Initially, additional workers contribute significantly to output, increasing productivity. However, as more workers are added, diminishing returns set in due to space limitations and fixed oven capacity.
Additional Insight:
- The Total Cost (TC) curve will be upward-sloping, reflecting increasing costs as more workers are hired.
- Since labor is the only variable cost, total cost is calculated as:
[
TC = \text{Fixed Costs} + \text{(Wage per Worker × Number of Workers)}
]
Initially, total cost rises slowly when output increases at an increasing rate, but as diminishing returns set in, total cost increases at a faster rate.
Thus, the production function follows the law of increasing marginal returns initially, followed by diminishing marginal returns, confirming the correct answer as True.