Question

You are a manager at Glass Inc.—a mirror and window supplier. Recently, you conducted a study of the production process for your single-side encapsulated window. The results from the study are summarized below and are based on the eight units of capital currently available at your plant. Workers are paid \(60 per unit, per unit capital costs are \)20, and your encapsulated windows sell for $12 each. Given this information, optimize your human resource and production decisions. Do you anticipate earning a profit or a loss? Explain carefully

Short answer

The firm must expect a profit of$\mathbf{\$}\mathbf{620}$ and needs to employ 6 laborers to maximize its profit.

Step-by-step solution

Explaining anticipated earning of a profit or a loss.

The mirror and window provider is a profit-maximizing company that will hire labor until the value of its marginal product matches the $\mathbf{\$}\mathbf{60}$ wage rate. At the moment, the facility has 8 units of capital accessible.

The only decision that the corporation is aware of is its desire for workers. The firm will continue to hire labor until the value of the marginal product of labor reaches $\mathbf{\$}\mathbf{60}\mathbf{,}$assuming a wage rate of$\mathbf{\$}\mathbf{60}$per unit of labor.

It is worth noting that this happens when it recruits six units of labor. The unit of labor adds 5 units of output to the firm, yielding $\mathbf{\$}\mathbf{60}\mathbf{,}$ which is the wage rate.

Captial	Labor	Output	Marginal product of labor	Variable cost	Fixed cost	Total cost	Total revenue	Profit
8	0	0	-	0	160	160	0	-160
8	1	10	10	60	160	220	120	-100
8	2	30	20	120	160	280	360	80
8	3	60	30	180	160	340	720	380
8	4	80	20	240	160	400	960	560
8	5	90	10	300	160	460	1080	620
8	6	95	5	360	160	520	1140	650
8	7	95	0	420	160	580	1140	560
8	8	90	-5	480	160	640	1080	440
8	9	80	-10	540	160	700	960	260
8	10	60	-20	600	160	760	720	-40
8	11	30	-30	660	160	820	360	-460

Calculating the profit of the firms based on this decision.

Profit is the difference between revenue and expense. A fixed cost of capital of $\mathbf{\$}\mathbf{20}$per unit and a variable cost of labor of $\mathbf{\$}\mathbf{60}$per unit make up the overall cost of the company. The market value of sales is used to calculate revenue, with the price per unit of encapsulated window sold being$\mathbf{\$}\mathbf{12}\mathbf{.}$

Therefore, the firm must expect a profit of$\mathbf{\$}\mathbf{620}$ and needs to employ 6 laborers to maximize its profit.