Question

You must show your work on all mathematical questions and I must be able to follow your steps.

Your assistant was called away for a medical emergency while he was working on Frosty Cola’s cost structure for last month. He was not able to finish his analysis; however, you have a meeting with the chief financial officer in fifteen minutes and he is expecting this information in its entirety. Your assistant was able to jot down the following for you before he left, shouting on his way out the door, “Remember, all labor units are paid equally and that’s our only variable input right now!”:   

a)

Labor	Q	Fixed Cost	Variable Cost	Total Cost
0	0	_____	$0	_______
1	11,000	_______	_______	_______
2	25,000	_______	_______	_______
3	49,500	_______	_______	_______
4	55,000	_______	$8,000	_______
5	58,400	_______	_______	$30,000

b)

The CFO is also interested in learning more about diminishing marginal returns. What would you tell him, and how would you explain where Frosty Cola first encounters this phenomenon?

c)

The CFO also wants to know what the average variable cost and the average total cost of the output is when the company produces 49,500 units. What would you tell him?

Answer 1

Answer

a) Let us first find the wage rate of labor, the only variable input.

When labor is 4 units, the variable cost = $8,000.

  When labor is 1 unit, the variable cost = $8,000 / 4 = $2,000

So, the wage rate of labor is $2,000 and this is the variable cost per unit of labor.

Now, we can calculate the variable cost for all units of labor in the following way;

When labor is 2 units, the variable cost = $2,000 * 2 = $4,000

Let us now calculate, the fixed cost.

Total Cost = Fixed Cost + Variable Cost

Fixed Cost = Total Cost - Variable Cost

From the table we see that, when output is 58,400 units, the total cost is $30,000.

  When output is 58,400 units, the fixed cost = $30,000 - $10,000 = $20,000

The fixed cost remains fixed for all units of output. Moreover at the beginning of production, when the output is zero, the firm has to bear the fixed cost. So, here the fixed cost is $20,000 for all levels of output.

Now, we can calculate the total cost by adding the fixed cost and variable cost.

When output (Q) is 11,000, the total cost = $20,000 + $2,000 = $22,000

The final table is shown below-

Table - 1

Labor	Q	Fixed Cost	Variable Cost	Total Cost
0	0	$20,000	$0	$20,000
1	11,000	$20,000	$2,000	$22,000
2	25,000	$20,000	$4,000	$24,000
3	49,500	$20,000	$6,000	$26,000
4	55,000	$20,000	$8,000	$28,000
5	58,400	$20,000	$10,000	$30,000

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b) The fixed input remains fixed in the short-run. At the initial stage of production, when the employment of variable input,here, labor increases, the output also increases but after a certain amount of labor, the output increases at a decreasing rate. This happens because, as of the inputs remains fixed in production, the gradual increase of variable input creates pressure on the fixed input and as a result, the fixed input becomes less productive. Thus, the hiring of an additional unit of labor generates less and less amount to the total output, i.e., the marginal productivity of labor gradually decreases. This is called the diminishing marginal returns.

In the following table, we will calculate the marginal productivity of labor(MPL) to see where Frosty Cola first encounters this phenomenon.

Marginal productivity of Labor = Change in output(Q) / Increase of an additional unit of labor(L) = Q/ L

Table - 2

Labor	Q	Marginal productivity of Labor
0	0	-
1	11,000	11.000
2	25,000	14,000
3	49,500	24,500
4	55,000	5,500
5	58,400	3,400

From the above table, we see that, the marginal productivity of labor increases till the 3 units of labor. After the 3 units of labor, when the firm hires the 4th unit of labor, the marginal productivity of labor starts to decrease. Thus, the Frosty Cola first encounters this phenomenon when it hires 4th unit of labor.

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c) Average Variable Cost = Total Variable Cost / Output

Average Total Cost = Total Cost / Output

From Table-1, we see that when the company produces 49,500 units of output, its total variable cost is $6,000 and the total cost is $26,000.

Average Variable Cost = $6,000 / 49,500 = $0.12(approx.)

Average Total Cost = $26,000 / 49,500 = $0.53(approx.)

So, when the company produces 49,500 units of output, the average variable cost and the average total cost of the output are approximately $0.12 and $0.53 respectively.

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