Question

PROBLEM ONE - Using the information in data set one, which I have included in the table below, recalculate total cost, fixed cost, variable cost, marginal cost, average total cost, average variable cost and average fixed costs if the price of the fixed input (the small stores rent) is not $200 but $220. A new lease may have caused the rent to increase. I have created Table 1 for you to put your answers in. Assume the price of the variable input, labor, is still $50 per unit.  When fixed costs change which other costs will increase? Compare the costs you calculate for table one to the costs calculated in the notes in chapter 7 to find the answer.

TABLE ONE FOR ANSWERS TO PROBLEM ONE

Units of Labor	Total Product (output)	FC	VC	TC	MC	ATC	AVC	AFC
0	0
1	3
2	7
3	12
4	16
5	19
6	21

Problem Two - Using the information in data set one, which I have included in the table below, recalculate total cost, fixed cost, variable cost, marginal cost, average total cost, average variable cost and average fixed costs if the price of the variable input (which is labor in this example) is not $50 but $55. I have created Table 2 for you to put your answers in. Assume that fixed costs remain at $220.  When the price of a variable input changes which other costs will increase? Compare the costs you calculate for table two to the costs calculated in table one to find your answers.

TABLE TWO FOR ANSWERS TO PROBLEM TWO

Units of Labor	Total Product (output)	FC	VC	TC	MC	ATC	AVC	AFC
0	0
1	3
2	7
3	12
4	16
5	19
6	21

Answer 1

Answer to Problem 1:

Units of Labor	Total Product	FC	VC	TC	MC	ATC	AVC	AFC
0	0	220	0	220	-	-	-	-
1	3	220	50	270	16.67	90	16.67	73.33
2	7	220	100	320	12.5	45.71	14.28	31.43
3	12	220	150	370	10	30.83	12.5	18.33
4	16	220	200	420	12.5	26.25	12.5	13.75
5	19	220	250	470	16.67	24.73	13.16	11.58
6	21	220	300	520	25	24.76	14.29	10.48

In order to calculate the missing values in the table we need to take into account information given in the table as well as the question. The question already gives you the fixed cost (the rent), $220, which stays fixed irrespective of the production or the units of labor employed. The only input in production is labor, which costs $50 per unit employed.

We use the following formulae to calculate the missing values:-

For Every Level of Labor Units Employed:-

Fixed Cost = $220

Variable Cost = Units of Variable Input * Price of Variable Input =  Units of Labor Employed * $50

Total Cost = Fixed Cost + Variable Cost

Marginal Cost = Change in Total Cost/Change in Total Product

Marginal cost reflects the increment in total cost for every additional unit of input employed. In this case, as fixed costs remains fixed at $220 at all levels of input and product, with every additional labor input only variable costs change i.e. by the additional cost of employing that unit of labor ($50). Hence we may also write the formula as the ratio of the change in variable costs to the change in total product. In this case change in total product is simply the difference between the total product before and after an additional unit of labor is employed.

Average Total Cost = Total Cost/Total Product

Average Variable Cost= Variable Cost/Total Product

Average Fixed Cost=Fixed Cost/Total Product

Note:When no labor is employed and total product is zero, marginal cost, average total cost, average variable cost and average fixed cost are undefined.

As we can see from above, fixed costs enter the formulae of Total Cost, Average Total Cost & Average Fixed Cost. Hence an increase in fixed cost will lead to a change in these three values at every level of labor employed.

However, as at every level of labor employed fixed costs remain the same, Change in Total Cost is equivalent to Change in Variable Cost. Therefore Marginal Costs are not affected by an increase in fixed cost.

Answer to Problem 2:

Units of Labor	Total Product	FC	VC	TC	MC	ATC	AVC	AFC
0	0	220	0	220	-	-	-	-
1	3	220	55	275	18.33	91.67	18.33	73.33
2	7	220	110	330	13.75	47.14	15.71	31.43
3	12	220	165	385	11	32.1	13.75	18.33
4	16	220	220	440	13.75	27.5	13.75	13.75
5	19	220	275	495	18.33	26.1	14.47	11.58
6	21	220	330	550	27.5	26.19	15.71	10.48

In this question, per unit cost of the variable input i.e. labor increase to $55 from $50. This will lead to higher variable costs and as a result, higher total cost, marginal cost, average variable cost and average total cost. Fixed cost remains the same at $220

We use the same set of formulae:-

For Every Level of Labor Units Employed:-

Fixed Cost = $220

Variable Cost = Units of Variable Input * Price of Variable Input =  Units of Labor Employed * $55

Total Cost = Fixed Cost + Variable Cost

Marginal Cost = Change in Total Cost/Change in Total Product

Marginal cost reflects the increment in total cost for every additional unit of input employed. In this case, as fixed costs remains fixed at $220 at all levels of input and product, with every additional labor input only variable costs change i.e. by the additional cost of employing that unit of labor ($50). Hence we may also write the formula as the ratio of the change in variable costs to the change in total product. In this case change in total product is simply the difference between the total product before and after an additional unit of labor is employed.

Average Total Cost = Total Cost/Total Product

Average Variable Cost= Variable Cost/Total Product

Average Fixed Cost=Fixed Cost/Total Product

Note:When no labor is employed and total product is zero, marginal cost, average total cost, average variable cost and average fixed cost are undefined.

As we can see from above, variable costs (i.e. cost of per unit labor) enter the formulae of Total Cost, Marginal Cost, Average Variable Cost and Average Total Cost. Hence an increase in variable cost will lead to an increase in all these variables at every level of labor employed.