# Cost of Production – Solved Question Paper

Review Questions 5

316-660 Managerial Economics

Microeconomics

TOPICS 4 AND 5

COSTS OF PRODUCTION

1. Consider the following data on short-run production. Assume that number of workers hired

(labour) is the only variable input:

Number of workers

0

1

2

3

4

Output

0

5

10

15

20

Suppose the wage that must be paid to hire each extra worker does not vary with number of

workers hired. Which of the following is correct?

a) The production function displays diminishing marginal product of labour.

b) The total cost curve will have constant gradient.

c) The gradient of total cost is increasing with output.

d) It is not possible to make any inferences about the gradient of the total cost curve without

also knowing the fixed cost.

2. Consider the following data on short-run production. Assume that number of workers hired

(labour) is the only variable input

Number of workers

0

1

2

3

4

Output

0

5

9

12

14

Suppose the wage that must be paid to hire each extra worker does not vary with number of

workers hired. Which of the following is not correct?

a) The production function exhibits diminishing marginal product of labour.

b) The gradient of the total cost curve is increasing with output.

c) Total cost increases with output.

d) The gradient of the total cost curve is a straight line.

3. (GKM, p.281) You own a painting company. In the short run the company has a total fixed

cost of $200, and the following schedule for Short-run Total Variable Cost:

Qty of Houses Short-run

Painted

Per Variable Cost

Month

($)

0

1

2

3

4

5

6

7

Short-run

Average Fixed

Cost

($)

Short-run

Short-run

Average

Average Total

Variable Cost Cost

($)

($)

0

10

20

40

80

160

320

640

Calculate short-run average fixed cost, short-run average variable cost, and short-run average

total cost for each quantity.

4. Rex Carr owns a junk yard which processes used cars into scrap metal. In the long-run Rex

can use two methods to destroy cars. The first involves purchasing a hydraulic car smasher

which costs $200 a year to own and then spending $1 for every car smashed; the second

method involves purchasing a hammer that will last one year and costs $40 and paying his

brother Otto Carr to destroy the cars at a cost of $5 each.

a) Draw a graph of short-run total cost, short-run average total cost, and short-run marginal

cost for each production method.

b) What is the minimum number of cars processed per year for which Rex should be willing

to purchase the hydraulic smasher?

5. The Milk Industry in Australia

‘The typical cost structure of producing milk might be broadly represented as: feed costs (40

per cent); dairy overheads including hired labour, imputed labour, land and administration

costs (19 per cent); milk levies and freight (15 per cent); other dairy variable costs including

fuel and oil and repairs (12 per cent); herd costs (7 per cent); and shed costs (7 per

cent).[p.51]

Table 1:

Year

1975

1980

1985

1990

1995

2000

Total number of

dairy

farms

(Australia)

30630

21994

19342

15396

14166

12888

Average size of

milking herd per

farm

77

85

93

107

134

155

Average milk yield

per cow (litres)

2623

2848

3336

3781

4550

5000

Table 2:

Victoria

NSW

Queensland

SA

WA

Tasmania

AUSTRALIA

Total

milk

production

(millions of litres)

6870

1395

848

713

412

609

10847

Average size of

total herd per farm

(2000)

252

225

185

219

304

285

242

From ACCC (2001), Impact of farmgate deregulation on the Australian milk industry: Study

of prices, costs and profits, accessed from www.accc.gov.au.

a) What would be classified as fixed costs and variable costs in the dairy milk industry?

b) Graph the relation between average size of milking herd per farm and average milk

production per cow. Suppose it is possible to interpret that relation as representing the longrun relation between inputs and average output for a dairy farm. How would you describe the

production technology?

Review Questions 5

316-660 Managerial Economics

Microeconomics

SOLUTIONS TO REVIEW QUESTIONS

TOPICS 4 AND 5:

COSTS OF PRODUCTION

1. Answer (b): Each extra worker adds the same amount to total output. Therefore it follows

that it takes the same amount of labour to produce each extra unit of output. With a constant

wage per worker, it will cost the same amount to produce each extra unit of output. Therefore

the total cost curve has a constant gradient.

2. Answer (e): This statement is incorrect. For total cost to be a straight line implies that each

extra unit of output will cost the same extra amount to produce as the previous unit. For this

to occur means that – with a constant wage to hire each extra worker – each extra worker

must add the same amount to total output. But in fact the data in the table show that each

extra worker adds a smaller amount to total output than the previous worker. (Hence the

gradient of the production function is decreasing with the quantity of output, and the gradient

of the total cost curve is increasing with the quantity of output.)

3.

Qty of Houses

Painted Per

Month

Short-run

Variable Cost

($)

0

1

2

3

4

5

6

7

0

10

20

40

80

160

320

640

AFC = $200/Qty

SRAVC = SRTVC/Qty

SRATC = AFC + SRAVC

4. a)

Average Fixed Short-run

Cost

Average

($)

Variable Cost

($)

Short-run

Average Total

Cost

($)

$200

$100

$66.66

$50

$40

$33.33

$28.57

$210

$110

$80

$70

$72

$86.66

$120

$10

$10

$13.33

$20

$32

$53.33

$91.42

Method 2 – SRTC

400

200

40

40

200

400

Number of cars

b) From the diagram above it can be seen that SR total cost of the first car wrecking method is

above SR total cost of the second car wrecking method where the number of cars wrecked is

less than 40; SR total cost is equal where the number of cars wrecked equals 40; and SR total

cost of the first car wrecking method is below SR total cost of the second car wrecking

method where the number of cars wrecked is greater than 40. Hence the number of cars

wrecked needs to be at least 40 in order for it to be worthwhile for Rex to purchase the

hydraulic smasher.

[Note that mathematically the total cost of the first method is 200 + C (where C = number of

cars wrecked); and total cost of the second method is 40 + 5C. These equations can be used

to solve for values of C for which total cost of the first method is less than/equal to/more than

total cost of the second method.]

5. The Milk Industry in Australia

a) Fixed costs – Land and administration costs; Shed costs.

Variable costs – Feed costs; Labour; Milk levies and freight; Fuel, oil and repairs; Herd costs.

[How you end up classifying each cost item is less important than that you do it based on the

logic of the definition of fixed and variable cost – That costs that you decide do not vary with

quantity of output are fixed, and costs that you decide do vary with quantity of output are

variable.]

b)

6000

Average milk yield

5000

4000

3000

2000

1000

0

0

50

100

150

200

Size of herd

Average milk yield increase with herd size. Hence we would say that the production

technology exhibits increasing returns to scale or (in terms of cost of production) economies

of scale.

[That average milk yield increases with herd size means that (on average) each extra cow

added to a herd causes a more than proportionate increase in total output

(= definition of ‘increasing returns to scale’). Assuming constant input prices, this in turn

means that the average cost of producing each extra litre of milk will decrease with total

quantity of milk produced. Therefore long-run average cost of production per litre of milk

will decline (= definition of ‘economies of scale’).]

[Note that the graph above is not a production function – But what we are doing in this

answer is using information about the long-run relation between inputs and average output,

which could easily be translated into a relation between size of herd and total output, to make

inferences about the nature of the production technology.]

…