# Introduction to Economics

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Introduction to Economics ­ECO401
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Lesson 5.6
BACKGROUND TO SUPPLY/COSTS (CONTINUED..............)
PROFIT MAXIMISATION
Economists say that when firms earn zero accounting profits, they actually earn normal
economic profits because TC already includes the normal profits that owners of the firms need
for themselves to stay in the business. Positive profits are, for this reason, called supernormal
profits as they are over and above what the owners normally require as a return for their
entrepreneurship.
Approaches of Profit Maximization:
Profit maximization can be studied using the TR-TC approach and the MR-MC approach.
i.  In the TR-TC approach it is assumed that firm is price maker and firm is operating
in short run. Total profit is the vertical distance between TR and TC.
ii. In the MR-MC approach, two steps are followed to identify maximum profit. First:
the profit-maximizing output is identified ­ this is the point where MR cuts MC.
Second: the size of maximum profit is calculated using AC and AR curves.
If MR & AR remain same over the long run, then the profit maximizing output will be obtained
where MR intersects LRMC.
If AC is always above AR, then firms will never be able to make a profit. In this case, the point
where MR=MC, represents the loss-minimizing point.
When MC and MR intersect at two points, not one, then Firms should produce at that point of
intersection of MR and MC beyond which, MC exceeds MR.
If a firm's AR is below its AVC, it will shut down since it is not covering any part of its fixed
costs.
Profit maximization using calculus:
If total revenue (TR) and total cost equation are given as follows:
TR = 48q ­ q2
TC = 12 + 16q + 3Q2
Then we can find out the value of output at which profit is maximized as under:
Solution:
Profit is maximized at the point where
MC = MR
MC function can be found by taking derivative of total cost function. i.e.:
MC = d TC / dQ
MC = 16 + 6Q
MR function can be found by taking derivative of total revenue (TR) function i.e.:
MR = d TR / dQ
= 48 ­ 2Q
As profit is maximized at the point where MR = MC, so by equating values of MC and MR
function, we get,
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Introduction to Economics ­ECO401
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MR =MC
16 + 6Q = 48 ­ 2Q
6Q + 2Q = 48 ­ 16
8Q = 32
Q=4
The equation for total profit is,
Tń = TR ­ TC
= 48Q ­ Q2 - (12 + 16Q + 3Q2)
= 48Q ­ Q2 ­ 12 ­ 16Q ­ 3Q2
= -4Q2 + 32Q ­ 12
Putting Q = 4, we get,
Tń = - 4(4)2 + 32 (4) ­ 12
= -64 + 128 - 12
Tń = 52
So profit is maximized where output is 4 and the maximum profit is 52.
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Introduction to Economics ­ECO401
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END OF UNIT 5 - EXERCISES
How will the length of the short run for a shipping company depend on the state of the
shipbuilding industry?
If the shipbuilding industry is in recession, the short run (and the long run) may be shorter. It
will take less time to acquire a new ship if there is no waiting list, or if there are already ships
available to purchase (with perhaps only minimal modifications necessary).
Up to roughly how long is the short run in the following cases?
(a) A mobile ice-cream firm. (b) A small grocery. (c) Electricity power generation.
a) 2-3 days: the time necessary to acquire new bicycles, equipment and workers.
b) Several weeks: the time taken to acquire additional premises.
c) 3-5 years: the time taken to plan and build a new power station.
How would you advise the naanwaala (bread-maker) next door as to whether he should
(a) employ an extra assistant on a Sunday (which is a high demand day); (b) extend his
shop, thereby allowing more customers to be served on a Sunday?
a) If maximizing profit is the sole aim, then he should employ an additional assistant if the
extra revenue from the extra customers that the assistant can serve is greater than the
costs of employing the assistant.
b) Only if the extra revenue from the extra customers will more than cover the costs of the
extension plus the extra staffing.
Given that there is a fixed supply of land in the world, what implications can you draw
from about the effects of an increase in world population for food output per head?
Other things being equal, diminishing returns would cause food output per head to decline (a
declining MPP and APP of labour). This, however, would be offset (partly, completely or more
than completely) by improvements in agricultural technology and by increased amounts of
capital devoted to agriculture: this would have the effect of shifting the APP curve upwards.
The following are some costs incurred by a shoe manufacturer. Decide whether each
one is a fixed cost or a variable cost or has some element of both.
(a) The cost of leather. (b) The fee paid to an advertising agency. (c) Wear and tear on
machinery. (d) Business rates on the factory. (e) Electricity for heating and lighting. (f)
Electricity for running the machines. (g) Basic minimum wages agreed with the union.
(h) Overtime pay. (i) Depreciation of machines as a result purely of their age
(irrespective of their condition).
(a) Variable. (b) Fixed (unless the fee negotiated depends on the success of the campaign).
(c) Variable (the more that is produced, the more the wear and tear). (d) Fixed. (e) Fixed if
the factory will be heated and lit to the same extent irrespective of output, but variable if the
amount of heating and lighting depends on the amount of the factory in operation, which in
turn depends on output. (f) Variable. (g) Variable (although the basic wage is fixed per
worker, the cost will still be variable because the total cost will increase with output if the
number of workers is increased). (h) Variable. (i) Fixed (because it does not depend on
output).
Assume that a firm has 5 identical machines, each operating independently. Assume
that with all 5 machines operating normally, 100 units of output are produced each day.
Below what level of output will AVC and MC rise?
20 units. Below this level, the one remaining machine left in operation will begin to operate at a
level below its optimum. (Note that with 5 machines producing 100 units of output, minimum
AVC could be achieved at 100, 80, 60, 40 and 20 units of output, but between these levels
some machines may be working at less than their optimum and some at more than their
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optimum. Thus if the optimum level for a machine is critical, then the AVC curve may look
`wavy' rather than a smooth line.
Why is the minimum point of the AVC curve (y) at a lower level of output than the
minimum point of the AC curve (z)?
Because between points y and z marginal cost is above AVC (and thus AVC must be past the
minimum point) but below AC (and thus AC cannot yet have reached the minimum point).
Even though AVC is rising beyond point y, the fall in AFC initially more than offsets the rise in
AVC and thus AC still falls.
What economies of scale is a large department store likely to experience?
Specialized staff for each department (saving on training costs and providing a more efficient
service for customers); being able to reallocate space as demand shifts from one product to
another and thereby reducing the overall amount of space required; full use of large delivery
lorries which would be able to carry a range of different products; bulk purchasing discounts;
Why are firms likely to experience economies of scale up to a certain size and then
diseconomies of scale after some point beyond that?
Because economies of scale, given that most arise from increasing returns to scale, will be
fully realized after a certain level of output, whereas diseconomies of scale, given that they
largely arise from the managerial problems of running large organizations, are only likely to set
in beyond a certain level of output.
How is the opening up of trade and investment between, say eastern and western
Europe, likely to affect the location of industries within Europe that have (a) substantial
economies of scale; (b) little or no economies of scale?
a) Given that production will take place in only one or two plants, new plants will tend to
be located near to the centre of the new enlarged European market.
b) Plants will still tend to be scattered round Europe, given that the customers are
scattered.
These effects will be the result of attempts to minimize transport costs and thus will be more
significant the higher are transport costs per kilometer.
Name some industries where external economies of scale are gained. What are the
specific external economies in each case?
Two examples are:
·  Financial services: pool of qualified and experienced labour, access to specialist
software, one firm providing specialist services to another.
·  Various parts of the engineering industry: pool of qualified and experienced labour,
Would you expect external economies to be associated with the concentration of an
industry in a particular region?
Yes. There may be a common transport and communications infrastructure that can be used;
there is likely to be a pool of trained and experienced labour in the area; joint demand may be
high enough to allow economies of scale to be experienced in the supply of some locally
extracted raw material.
If factor X costs twice as much as factor Y (Px/Py = 2), what can be said about the
relationship between the MPPs of the two factors if the optimum combination of factors
is used?
MPPx/MPPy = 2. The reason is that if MPPx/Px = MPPy/Py, then, by rearranging the terms of
the equation, MPPx/MPPy must equal Px/Py (= 2).
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Could isoquants ever cross?
Not for a given state of technology, otherwise it would mean that at one side of the intersection
the higher output isoquant would be `south-west' of the lower output isoquant. This would
mean that a higher output could be achieved by using less of both factors of production!
Could they ever slope upward to the right?
Yes. It would mean that one of the two factors had a negative marginal productivity that was
greater than the positive marginal productivity of the other: i.e. that MPPa/MPPb (or
MPPb/MPPa) was negative (a negative marginal rate of factor substitution).
This situation will occur when so much is used of one factor that diminishing returns have
become so great as to produce substantial negative marginal productivity: isoquants will bend
back on themselves beyond the points where they become vertical or horizontal. The firm,
however, will not produce along this portion of an isoquant, because the price ratio (Pa/Pb) will
(virtually) never be negative.
What will happen to an isocost if the prices of both factors rise by the same
percentage?
It will shift inwards parallel to the old isocost.
Why do the prices of cattle and sheep prices fall so drastically "on", or just "after" the
first day of Eid-ul-Azha?
The supply curve for cattle and sheep is fixed in the short-run, i.e. a vertical supply curve,
therefore price will be determined by demand. Since demand for "cattle for sacrifice" falls
drastically after or on the first day of Eid-ul-Azha, the price has to come down drastically as
well for the market to clear.
Explain the shape of the LRMC curve for a firm with a typical U-shaped LRAC curve.
At first economies of scale cause the LRMC to fall. Then because of (marginal) diseconomies
of scale, additional units of production begin to cost more to produce than previous units: the
LRMC begins to slope upwards. But the LRAC is still falling because the LRMC is below it
pulling it down. It is not until the LRMC crosses the LRAC that the firm will experience a rising
LRAC and hence average diseconomies of scale.
Will the "envelope curve" be tangential to the bottom of each of the short-run average
cost curves? Explain why it should or should not be.
No. At the tangency points the two curves must have the same slope. Thus the slope at the
tangency point is not zero (the slope at the turning point or minima of the SRAC curves).
What would the isoquant map look like if there were (a) continuously increasing returns
to scale; (b) continuously decreasing returns to scale?
a) The isoquants would get progressively closer and closer together.
b) The isoquants would get progressively further and further apart.
What can we say about the slope of the TR and TC curves at the maximum profit point?
What does this tell us about marginal revenue and marginal cost?
The slopes are the same. But given that the slope of the total curve gives the respective
marginal, this means that marginal revenue will be equal to marginal cost.
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Introduction to Economics ­ECO401
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Fill in the missing figures in the table below.
TΠ
AΠ
Q
P=
TR
MR
TC
AC
MC
AR
0
9
6
1
8
10
2
7
12
3
6
14
4
5
18
5
4
25
6
3
36
7
2
56
TΠ
AΠ
Q
P = AR
TR
MR
TC
AC
MC
0
9
0
6
­
­6
­
8
4
1
8
8
10
10
­2
­2
6
2
2
7
14
12
6
2
1
4
2
3
6
18
14
4.3
4
1.3
2
4
4
5
20
18
4.5
2
0.5
0
6
5
4
20
25
5
­5
­1
­2
9
6
3
18
36
6
­18
­3
­4
16
7
2
14
56
8
­42
­6
Why should the figures for MR and MC be entered in the spaces between the lines?
Because marginal revenue (or cost) is the extra revenue (or cost) from moving from one quantity
to another.
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Introduction to Economics ­ECO401
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You are given the following information for a firm.
Q
0
1
2
3
4
5
6
7
P
12
11
10
9
8
7
6
5
TC
2
6
9
12
16
21
28
38
Construct a detailed table like the one you constructed in the earlier question with TR, AC,
MR, TC, AC, MC, TΠ and AΠ. Use your table to draw "two" diagrams (one with the marginal
revenue and cost curves, and one with the total (or average) revenue and cost curves) and
use them to show the "profit-maximising output" and the "level of maximum profit",
respectively. Confirm your findings by reference to the table you construct.
TΠ
AΠ
Q
P = AR
TR
MR
TC
AC
MC
0
12
0
2
­
­2
­
11
4
1
11
11
6
6
5
5
9
3
2
10
20
9
4.5
11
5.5
7
3
3
9
27
12
4
15
5
5
4
4
8
32
16
4
16
4
3
5
5
7
35
21
4.2
14
2.8
1
7
6
6
36
28
4.7
8
1.3
­1
10
7
5
35
38
5.4
­3
­0.4
The curves will be a similar shape to those discussed in the lecture, and included in the slides
handout. The peak of the TΠ curve will be at Q = 4. This will be the output where MR and MC
intersect.
Will the size of normal `profit' vary with the general state of the economy?
Yes. Normal profit is the rate of profit that can be earned elsewhere (in industries involving
similar level of risk). When the economy is booming, profits will normally be higher than when
the economy is in recession. Thus the `normal' profit that must be earned in any one industry
must be higher to prevent capital being attracted to other industries.
Given the following equations:
TR = 72Q ­ 2Q˛; TC = 10 + 12Q + 4Q˛
Calculate the maximum profit output and the amount of profit at that output using both
methods.
(a) TΠ = 72Q ­ 2Q˛ ­ 10 ­ 12Q ­ 4Q
= ­10 + 60Q ­ 6Q˛
(1)
dTΠ /dQ = 60 ­ 12Q
Setting this equal to zero gives:
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Introduction to Economics ­ECO401
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60 ­ 12Q = 0
12Q = 60
Q=5
(b) MR = dTR/dQ = 72 ­ 4Q
MC = dTC/dQ = 12 + 8Q
Setting MR equal to MC gives:
72 ­ 4Q = 12 + 8Q
12Q = 60
Q=5
To find the level of maximum profit, we must substitute Q = 5 into equation (1). This gives:
TΠ = ­10 + (60 × 5) ­ (6 × 5˛)
= ­10 + 300 ­ 150
= Rs. 140
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