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.]
…