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Introduction to Economics ECO401

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,

Introduction to Economics ECO401

MR =MC

16 + 6Q = 48 2Q

6Q + 2Q = 48 16

8Q = 32

Q=4

The equation for total profit is,

Tñ = TR TC

= 48Q Q2 - (12 + 16Q + 3Q2)

= 48Q Q2 12 16Q 3Q2

= -4Q2 + 32Q 12

Putting Q = 4, we get,

Tñ = - 4(4)2 + 32 (4) 12

= -64 + 128 - 12

Tñ = 52

So profit is maximized where output is 4 and the maximum profit is 52.

Introduction to Economics ECO401

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).

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

Introduction to Economics ECO401

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;

reduced administrative overheads as a proportion of total costs.

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,

access to specialist suppliers, possible joint research, specialized banking services.

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).

Introduction to Economics ECO401

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.

Introduction to Economics ECO401

Fill in the missing figures in the table below.

TΠ

AΠ

TΠ

AΠ

P = AR

4.3

1.3

4.5

0.5

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.

Introduction to Economics ECO401

You are given the following information for a firm.

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

P = AR

4.5

5.5

4.2

2.8

4.7

1.3

5.4

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 2Q²; TC = 10 + 12Q + 4Q²

Calculate the maximum profit output and the amount of profit at that output using both

methods.

(a) TΠ = 72Q 2Q² 10 12Q 4Q

= 10 + 60Q 6Q²

(1)

∴ dTΠ /dQ = 60 12Q

Setting this equal to zero gives:

Introduction to Economics ECO401

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 × 5²)

= 10 + 300 150

= Rs. 140

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