Question

The A-1 Corporation supplies airplane manufacturers with preformed sheet metal panels that are used on the exterior of aircraft. Manufacturing these panels requires only five sheet metal–forming machines, which cost \(500 each, and workers. These workers can be hired on an as-needed basis in the labor market at \)9,000 each. Given the simplicity of the manufacturing process, the preformed sheet metal panel market is highly competitive. Therefore, the market price for one of A-1’s panels is $80. Based on the production data in the accompanying table, how many workers should A-1 hire to maximize its profits?

Short answer

Table T1 shows that profits are maximized when a company employs five workers. Selling$\mathbf{1}\mathbf{,}\mathbf{600}$ units of sheet metal earns$\mathbf{\$}\mathbf{128}\mathbf{,}\mathbf{000}\mathbf{,}$ compared to a manufacturing cost of only $\mathbf{\$}\mathbf{47}\mathbf{,}\mathbf{500}\mathbf{.}$Therefore, the highest profit achieved is $\mathbf{\$}\mathbf{80}\mathbf{,}\mathbf{500}\mathbf{.}$

Step-by-step solution

Explanation

As a profit maximization company, aircraft manufacturers hire workers until the value of their marginal labor products equals the wage rate $\mathbf{\$}\mathbf{9}\mathbf{,}\mathbf{000}\mathbf{.}$ This means that the company will continue to hire workers until the value of the marginal product of labor reaches $\mathbf{\$}\mathbf{9}\mathbf{,}\mathbf{000}\mathbf{.}$ Currently, there are five capital units available in the form of sheet metal forming machines.

Calculation

Using Table T1, note that this is the case when 5 units of workers are employed. The fifth worker adds 120 units of production and brings the company $9,600. This is very close to the market that dominates the wage rate. Note that the sixth unit will yield only $6,400, which is quite less than the wage rate of $9,000.

Capital	Labor	Output	Marginal Product of Labor	Value of Marginal Product of Labor	Variable cost	Fixed cost	Total cost	Total revenue	Profit
5	0	0	-	0	0	2500	2500	0	-2500
-5	1	600	600	48000	9000	2500	11500	48000	36500
5	2	1,000	400	32000	18000	2500	20500	80000	59500
5	3	1,290	290	23200	27000	2500	29500	103200	73700
5	4	1,480	190	15200	36000	2500	38500	118400	19900
5	5	1,600	120	9600	45000	2500	47500	128000	80500
5	6	1,680	880	6400	54000	2500	56500	134400	77900

Table T1 shows that profits are maximized when a company employs five workers. Selling 1,600 units of sheet metal earns $128,000 compared to a manufacturing cost of only $47,500. Therefore, the highest profit achieved is $80,500.