Question

Suppose you are given the following partially complete table. You have a meeting with the chief financial officer in fifteen minutes and he is expecting this information in its entirety. Note: all labor units are paid equally and labor is the firm’s only variable input.     

             Labor               Q              Fixed Cost       Variable Cost              Total Cost                   

            =========================================================          

            0                      0                      ______                        $0                    ______           

            1                      1,500               ______                        ______            ______

            2                      4,500               ______                        ______            ______

            3                      6,000               ______                        ______            ______

            4                      7,200               ______                        $400                ______

            5                      8,000               ______                        ______            $7,500

b) The CFO is also interested in learning more about diminishing marginal returns. What would you tell him, and how would you explain where your company first encounters this phenomenon? Additionally, at which worker do diminishing marginal returns BEGIN?

c) The CFO also wants to know what the average fixed cost and the average total cost of the output is when the company produces 8,000 units. What would you tell him?

Answer 1

Answer

In the question, it is said that labor is the only variable input, and all labors are paid equally. Keeping this in mind, calculating the fixed cost, variable cost, and total cost in bold numbers, and completing the table as follows:

Labor	Quantity(Q)	Fixed Cost	Variable Cost	Total Cost
0	0	$7000	$0	$7000
1	1500	$7000	$100	$7100
2	4500	$7000	$200	$7200
3	6000	$7000	$300	$7300
4	7200	$7000	$400	$7400
5	8000	$7000	$500	$7500

We see, that for 4 units of labor, the variable cost is $400. As labors are paid equally, so per unit labor cost is $100 ($400/4).

Total Cost = Total Fixed Cost + Total Variable Cost

When quantity of output is 8000 units, total cost is $7500 , given

, for 8000 units of output,fixed cost = $7500 - $500 = $7000 ( fixed cost = total cost- variable cost)

As fixed cost is fixed for whatever be the quantity of production, so fixed cost is $7000 for all units of output. The firm has to bear fixed cost even for the '0' level of output. So for quantity '0' also, the fixed cost is $7000.

When the firm initiates its production, the only cost it bears is the fixed cost.So the total cost is only the fixed cost. So for '0' level of output, total cost, and total fixed cost both are same, as $7000.

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b) Diminishing Marginal Returns- In short-run, when one factor of production remains fixed, the marginal product of variable factor first increases, then reaches maximum, and then diminishes.

In the example, labor is the only variable input.

The marginal productivity of labor = MP_L = Q/L

In the following table, we calculate the MP_L for each additional unit of labor ,and it is shown in column 3.

Labor	Quantity(Q)	Marginal Productivity of Labor(MPL)
0	0	0
1	1500	1500
2	4500	3000
3	6000	1500
4	7200	1200
5	8000	800

From the table we see, that as the labor is increased by 1 units, the marginal returns of labor first rises till 2 units of labor, and then it diminishes.So here we observe the diminishing marginal returns after 2 units of labor, i.e. by adding one more unit of labor (2+1=3), the MP_L declines. The company encounters the diminishing marginal returns.

A  company with one fixed input , and one variable input may does not encounter it (diminishing marginal returns) first time. With one fixed input, the marginal productivity of variable input first rises because of the higher productivity of the fixed input.But with the more usage of the fixed input/factor, its productivity gradually declines, as the pressure on that input rises, and so the productivity of additional variable input declines, here labor. The marginal cost also diminishes initially, then it reaches minimum, when MP_L  is maximum, and them marginal cost rises with the fall of the MP_L..

At 3 units of labor, diminishing marginal returns begin.

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c) Average Fixed Cost = Total Fixed Cost/Total Units of Output

Average Variable Cost = Total variable Cost/ Total Units of Output

At 8000 units of output, Total Fixed Cost is $7000

Average fixed cost = $7000/8000 = $7/8 = $ 0.875

At 8000 units of output, Total Variable Cost is $500

Average variable cost = $500/8000 = $0.0625

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