Business Economics Sessions 3 & 4

Session 3

Imperial College Business School

Business Economics

1

Professor David Shepherd

Reading:

Pindyck and Rubenfeld, Chapters 3 & 4

Sexton, Chapters 4 &5


Consumer Theory:Preferences, Constraints and Choices

2

Available Alternatives

Market basket (or bundle) Lists specific quantities of one or more goods that a consumer might buy. To explain the theory of consumer behavior, we will ask whether consumers prefer one market bundle to another

A 20 30

B 10 50

D 40 20

E 30 40

G 10 20

H 10 40

Market Bundle Units of Food Units of Clothing

.

Consumer Preferences: Assumptions

Completeness: Preferences are assumed to be complete. In other words, consumers can compare and rank all possible bundles. Thus, for any two market bundles A and B, a consumer will either prefer A to B, prefer B to A, or be indifferent between the two. Indifference means that a person is equally satisfied with either bundle

Transitivity: Preferences are transitive. Transitivity means that if a consumer prefers bundle A to bundle B and bundle B to bundle C, then the consumer also prefers A to C. Transitivity implies consumer consistency in consumer decision-making

More is better than less: Consumers always prefer more of any good to less. In addition, consumers are never satisfied or satiated; more is always better, even if just a little better

Consumer Preferences: Indifference Curves

The consumer prefers bundle E, which lies above U1, to A, but prefers A to H or G, which lie below U1.

The indifference curve shows the bundles of goods that give the same level of utility (satisfaction)

An indifference map is a set of indifference curves that describes a person's preferences.

Higher indifference curves show higher utility

Any bundle on indifference curve U3, such as A, is preferred to any bundle on curve U2 such as B, which in turn is preferred to any bundle on U1, such as D.

The Indifference Map

indifference map: a set of indifference curves showing the market bundles between which a consumer is indifferent.

The indifference map is a mapping of consumer preferences and it must satisfy our assumptions about those preferences.

For example, if indifference curves U1 and U2 intersect, our assumptions are violated.

According to this diagram, the consumer should be indifferent between bundles A and B, and A and D, and transitivity therefore implies indifference between A and D. But B should be preferred to Dbecause B has more of both goods.

So our assumptions imply indifference curves can not intersect.

Preferences and the Indifference Map

The magnitude of the slope of an

indifference curve measures the

consumers marginal rate of substitution (MRS) between two goods.

In this figure, the MRS between

clothing (C) and food (F) falls from 6

(between A and B) to 4 (between B and

D) to 2 (between D and E) to 1

(between E and G)

Convexity. When the MRS diminishes

along an indifference curve, the curve

is convex. The assumption of convexity

implies that the more of one good the

consumer has ( food), the less willing

he or she is to give up the other good

(clothing) and vice versa

The Marginal Rate of Substitution in Consumption

marginal rate of substitution: the amount of a good that a consumer is

willing to give up in order to obtain one additional unit of another good.

Budget Constraints

The indifference map shows how consumer preferences are ordered, but to determine what a consumer will actually buy we need to know how much income is available to spend and the prices of the goods. Income is limited and so the consumer faces a budget constraint. The budget constraint shows all combinations of goods for which the total amount of money spent is equal to available income.Suppose income is $80 and food and clothing are priced at $1 and $2 respectively. We can then calculate the bundles the consumer can afford to buy.

Market Bundles and the Budget Constraint

Market Bundle Food (F) Clothing(C) Total Spending

A 0 40 $80

B 20 30 $80

D 40 20 $80

E 60 10 $80

G 80 0 $80

The Budget Line

A budget line describes the combinations of goods that can be purchased given the consumers income and the prices of the goods.

Line AG (which passes through points B, D, and E) shows the budget associated with an income of $80, a price of food of PF = $1 per unit, and a price of clothing of PC = $2 per unit.

The slope of the budget line (measured between points B and D) is PF/PC = 10/20 = 1/2.

A Budget Line

Changes in Household Income

Income changes A change in income (with prices unchanged) causes the budget line to shift parallel to the original line (L1).

When the income of $80 (on L1) is increased to $160, the budget line shifts outward to L2.

If the income falls to $40, the line shifts inward to L3.

Effects of a Change in Income on the Budget Line

Changes in Prices

A change in the price of one good (with income unchanged) causes the budget line to rotate

When the price of food falls from $1.00 to $0.50, the budget line rotates outwards from L1 to L2.

However, when the price increases from $1.00 to $2.00, the line rotates inwards from L1to L3.

Effects of a Change in Price on the Budget Line

Consumer Choice

The consumer chooses bundle A where the budget line and indifference curve U2 are tangential.

No higher level of satisfaction (e.g., bundle D) can be attained, given the consumers income and for any other bundle on the budget line the consumer would reach a lower level of satisfaction (a lower indifference curve)

At point A, the MRS between the two goods equals the price ratio: MRS = Pf / Pc = 1 / 2

Maximizing Consumer SatisfactionThe consumer aims to achieve maximum satisfaction from consumption (utility maximization). The choice must satisfy two conditions: it must be located on the budget line and it must give the consumer the most preferred combination of goods and services.

The Impact of a Price Change: Normal Goods

Income and Substitution Effects: Normal Good

A decrease in the price of food has both an income effect and a substitution effect.

The consumer is initially at A, on budget line RS.

When the price of food falls, consumption increases by F1F2 as the consumer moves to B.

The substitution effect F1E (associated with a move from A to D) changes the relative prices of food and clothing but keeps real income (satisfaction) constant.

The income effect EF2 (associated with a move from D to B) keeps relative prices constant but increases purchasing power.

Food is a normal good because the income effect EF2 is positive.

The Impact of a Price Change: Inferior Goods

Income and Substitution Effects: Inferior Good

The consumer is initially at A on budget line RS.

With a decrease in the price of food, the consumer moves to B.

The resulting change in food purchased can be broken down into a substitution effect, F1E (associated with a move from A to D), and an income effect, EF2 (associated with a move from D to B).

In this case, food is an inferior good because the income effect is negative.

However, because the substitution effect exceeds the income effect, the decrease in the price of food leads to an increase in the quantity of food demanded.

Individual and Market Demand

Summing Individual Demands to Obtain a Market Demand Curve

The market demand curve is obtained by summing individual consumers demand curves, such as DA, DB, and DC.

At each price, the quantity of coffee demanded in the market is the sum of the quantities demanded by each consumer.

At a price of $4, for example, the quantity demanded by the market (11 units) is the sum of the quantity demanded by A (no units), B (4 units), and C (7 units).

Marginal Consumption Benefits

Using this interpretation , we can then say that satisfaction is maximized when the marginal benefitthe benefit associated with the consumption of one additional unit of foodis equal to the cost of obtaining that unit.

Given the relative prices of food and cloth, the consumer reaches his or her most preferred position by consuming at the point where MRS = PF/PC . The MRS can be thought of as measuring the marginal benefit the consumer obtains from the consumption of the last unit each product purchased and the relative price is the cost of obtaining that unit.

The vertical height of the demand curve shows the max prices consumers would pay to obtain additional units of output. These price valuations reflects the perceived marginal benefits.

The demand curve is downward-sloping because increased consumption of the product implies that additional units are valued less highly


Marginal Consumption Benefits and the Demand Curve

D (marginal benefit)

Q

P

P1

The downward slope of the demand curve reflects diminishing MRS. As the consumer has more of this product, additional units are valued less highly and the consumer will only buy them if the price is lower

18

Consumer Surplus

Consumer surplus Difference between what a consumer is willing to pay for a good and the amount actually paid.

Consumer surplus is the total benefit from the consumption of a product, less the total cost of purchasing it.

Here, the consumer surplus associated with six concert tickets (purchased at $14 per ticket) is given by the yellow-shaded area:

$6 + $5 + $4 + $3 + $2 + $1 = $21

Consumer Surplus and the Demand Curve

For the market as a whole, consumer surplus is measured by the area under the demand curve and above the line representing the purchase price of the good.

Here, the consumer surplus is given by the yellow-shaded triangle and is equal to 1/2 ($20 $14) 6500 = $19,500.

When the market price is lower consumers are better off because they can buy more units a cheaper price. Can we get a money measure of how much they gain from a price fall, or how much worse off they would be if the price went up. One way is to examine how consumer surplus changes.

Imperial College Business School 21

Price Changes and Consumer Surplus

D (marginal benefit)

Quantity

Price

P1

P2

a

b

At P1 consumer surplus = a b P1

At P2 consumer surplus = a c P2

The price fall generates an increase in consumer surplus

CS = P1 b c P2c

22

End of Session 3

Session 4


Business Economics

23

Professor David Shepherd

Reading:

Pindyck and Rubenfeld, Chapters 6 & 7

Sexton, Chapter 11


Production Choices and Production Costs

24

Units of output are produced when firms use labour and capital and a given technology in production processes which involves the transformation of inputs into outputs

The inputs are raw materials, components and energy

The outputs are the products that come out of the production process

The firms production costs are the total of all costs incurred in the production process, including the costs associated with the use of labour and capital as well as the cost of materials

To determine the behaviour of production costs we need to examine the nature of the production process and how labour and capital costs influence the production decision


The Production Process

The Technology of Production

The Production Function:

Production Periods

Short run Period of time during which quantities of one or more of the factors of production cannot be changed. The fixed factors are usually taken to be capital and technology

Long run Period during which all of the factors of production can be changed. In the log run all of the productive factors are variable

Q = f (L, K) A

Labour and Capital Productivity

Q = f(L,K)A

The marginal product of labour is the extra output produced by an extra unit of labour, holding capital constant

Q

=

= MPL

The marginal product of capital is the extra output produced by and extra unit of capital, holding labour constant

=

= MPK

LABOR INPUT

Production with Variable Capital and Labour

Production with Two Variable Inputs

CAPITALI

NPUT

1 2 3 4 5

1 20 40 55 65 75

2 40 60 75 85 90

3 55 75 90 100 105

4 65 85 100 110 115

5 75 90 105 115 120

Isoquant a curve showing all possible combinations of inputs that yield the same output

The Isoquant Map

Isoquant map Mapping of a number of isoquants, used to describe a production function.

A set of isoquants, or isoquant map, describes the firms production function.

Output increases as we move from isoquant q1 (at which 55 units per year are produced at points such as A and D),

to isoquant q2 (75 units per year at points such as B) and

to isoquant q3 (90 units per year at points such as C and E).

The Marginal Rate of Technical Substitution

Isoquants are downward sloping and convex. The slope at any point measures the MRTS, which shows the terms on which the firm can replace capital with labor (or vice versa) while maintaining the same level of output.

MRTS= (K/)

On isoquant q2, the MRTS falls progressively:

2/1 = 2

1/1 = 1

(2/3)/1 = 2/3

(1/3)/1 =1/3

Marginal Rate of Technical Substitution (MRTS) is the amount by which one input can be reduced when an extra unit of the other input is used, so that output remains constant.

MRTS = Change in capital input/change in labor input

= K/L (for a fixed level of q)

Production Functions: A Special Case

When the isoquants are straight lines, the MRTS is constant. Thus the rate at which capital and labor can be substituted for each other is the same no matter what level of inputs is being used.

Points A, B, and C represent three different capital-labor combinations that generate the same output q3.

Isoquants When Inputs Are Perfect Substitutes

Production Functions: Another Special Case

When the isoquants are L-shaped, only one combination of labor and capital can be used to produce a given output (as at point A on isoquant q1, point B on isoquant q2, and point C on isoquant q3). Adding more labor alone does not increase output, nor does adding more capital alone.

The fixed-proportions production function describes situations in which methods of production are limited.

Isoquants When Inputs Can Only Be Used In Fixed-Proportions

Production with Variable Capital and Labour:Returns To Scale

Returns to scale is a term to describe the rate at which output rises as inputs are both increased in the same proportion

Increasing returns to scale Situation in which output more than doubles when all inputs are doubled

Constant returns to scale Situation in which output doubles when all inputs are doubled

Decreasing returns to scale Situation in which output less than doubles when all inputs are doubled

Returns To Scale on the Isoquant Map

When a firms production process exhibits constant returns to scale as shown by a movement along line 0A in part (a), the isoquants are equally spaced as output increases proportionally.

However, when there are increasing returns to scale as shown in (b), the isoquants move closer together as inputs are increased along the line.

Output with Fixed Capital:

Diminishing Marginal Labour Productivity

Holding the amount of capital fixed at a particular level (say 3) we can see that each additional unit of labour generates less and less additional output. In other words, the marginal product of labour declines as output rises when K is held constant

Labour and Capital Costs

In the long run the firm can alter both its capital and labor inputs and move to a different scale of production

To determine the best combination of labor and capital the firm needs to look at the cost of labor relative to the cost of capital

The cost of a unit of labor is the market wage rate w

If capital is purchased, the cost of using that capital is the interest rate cost of the money used to buy it, plus any depreciation cost. If capital is rented, the cost is the rental cost.

If capital markets are efficient we would expect the rental cost and user cost of capital to be the same

So we think of the cost of capital in general as r which is either the rental cost or the interest plus depreciation cost

Producing at Minimum Cost

Firms will want to produce output at the lowest possible cost. How does a firm select the capital and labour inputs to produce a given output at minimum cost?

Leaving material costs to one side just for the moment, the firm has to consider the productivity of the labor and capital it could use in the production process and the cost of hiring those inputs

The total cost C of producing a given quantity of output is the sum of the labour cost and the capital cost:

C= w L + r K

This information can be combined with the isoquant map to determine the input choice associated with any quantity of output


The Isocost Line

The total cost of producing any quantity of output depends on the wage rate and the quantity of labour used and the cost of capital and the quantity of capital used

C= w L + r K

The total cost equation can be re-arranged as

K = C/r (w/r)

For a given value of C, this equation is called the isocost equation, or the isocost line, because it shows the different combinations of L and K which generate the same cost C

The isocost line has a slope of K/L = (w/r)

The slope is therefore the ratio of the wage rate to the cost of capital

The Cost Minimizing Input Choice

Isocost lines describe the combination of inputs that cost the same amount to the firm

Isocost curve C1 is tangent to isoquant q1 at A and shows that output q1 can be produced at minimum cost with labor input L1and capital input K1

Other input combinations-L2, K2 and L3, K3-yield the same output but at higher cost.

Input Substitution When Input Prices Change

Facing an isocost curve C1, the firm produces output q1 at point Ausing L1 units of labor and K1 units of capital.

When the price of labor is higher, relative to the price of capital the isocost curve is steeper and output q1is produced at point Bon isocost curve C2using less labour and more capital.

Units of output are produced by firms using labour and capital in a production process which involves the transformation of inputs into outputs

The firms production costs are the total of all costs incurred in the production process

These costs include capital costs, labour costs, and the cost of obtaining materials, components and energy. They also include the costs associated with the time and money that the owners of the firm have put into the business

The behaviour of production costs depends on the cost of hiring the inputs used and their productivity


Production Costs

Most of the costs incurred in production are direct costs. These are costs which involve a direct outlay of money by the firm when it buys or hires inputs

The firm may also incur implicit costs. These are costs which do not involve an outlay of money, but which should still be included as part of the firms production costs

If the owners the firm invest time and money in the business and do nottake a direct money payment there is still an opportunity cost incurred,because a return on that time and money could have been obtained byinvesting it elsewhere. That alternative return is the implicit cost incurredand it should be included in production costs, to get an accurate figure ofthe true cost of doing business.


Direct and Indirect Costs

The short run is defined as a period of time during which some of the inputs to the production process are fixed

The fixed inputs are the firms capital inputs (machinery, equipment, establishment size, etc.) and the available technology (production methods and know-how)

During the short run, the firm can alter production only by changing the amount labour employed and the use of materials, energy, etc

The inputs that can be changed are the firms variable inputs

This means that the firms production costs in the short run can be classified as either fixed costs or variable costs


Short-Run Production Costs

Total Costs are the sum of fixed costs and variable costs

TC = FC + VC

Average Cost is total cost per unit of output produced

AC= TC/Q

Average Fixed Cost is fixed cost per unit of output produced

AFC = FC/Q

Average Variable Cost is variable cost per unit of output produced

AVC = VC/Q

And the components of average total cost are:

AC = AFC + AVC


Average Costs

Marginal Cost shows how production costs change as output changes

Marginal cost is defined as the change in total cost arising from the production of an extra unit of output

MC = TC/Q

In the short run, capital costs are fixed, which means that they do not change when output changes

The only cost component that changes in the short run is variable cost and hence marginal cost is equivalent to the change in variable cost incurred when output expands

MC = VC/Q


Marginal Cost

Marginal and Average Cost:A Numerical Example

Rate of Fixed Variable Total Marginal Average Average Average

Output Cost Cost Cost Cost Fixed Cost Variable Cost Total Cost

(Units (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars

per Year) per Year) per Year) per Year) per Unit) per Unit) per Unit) per Unit)

(FC) (VC) (TC) (MC) (AFC) (AVC) (ATC)

(1) (2) (3) (4) (5) (6) (7)

0 50 0 50 -- -- -- --

1 50 50 100 50 50 50 100

2 50 78 128 28 25 39 64

3 50 98 148 20 16.7 32.7 49.3

4 50 112 162 14 12.5 28 40.5

5 50 130 180 18 10 26 36

6 50 150 200 20 8.3 25 33.3

7 50 175 225 25 7.1 25 32.1

8 50 204 254 29 6.3 25.5 31.8

9 50 242 292 38 5.6 26.9 32.4

10 50 300 350 58 5 30 35

11 50 385 435 85 4.5 35 39.5

MC includes all of the firms costs that vary with output

In the short run, capital costs are fixed, which means that they do not change when output changes

The behaviour of marginal cost depends only on the behaviour of the variable cost components, which are primarily the costs of labour, and materials and components and energy

If material and component costs are the same for each unit produced, this component of MC is constant

But what about labour costs?


The Components of Marginal Cost

Labor Costs and Marginal Cost

When output rises by Q, the extra labor cost incurred is the unit input cost of labor (the wage rate w) times the number of extra labor units (L) needed to produce that extra output. Ignoring material costs, the change in variable cost when output rises (i.e. Marginal Cost) is the same as the change in labor cost and hence VC/ Q = w L/ Q

The extra labor needed to obtain an extra unit of output is L/QWe have already defined the Marginal Product of Labor as MPL = Q/L and so L/Q = 1 / MPL. The implication is that MC is determined by the behavior of MPL

MC = VC/ Q = w L/ Q = w (1/MPL) = w / MPL

In the short run, with K fixed, it is usual to suppose that it becomes increasingly difficult for the firm to utilize extra labor efficiently and that MPL eventually declines as output rises and more labor is employed. This means that even if material costs per unit of output remain constant, the diminishing marginal productivity of labor must eventually cause marginal cost to rise as output rises

The Firms Short- Run Cost Curves

In (a) total cost TC is the vertical sum of fixed cost FC and variable cost VC.

In (b) average total cost ATC is the sum of average variable cost AVC and average fixed cost AFC.

Marginal cost MC crosses the average variable cost and average total cost curves at their minimum points.

50

Unit Costs: Key Information

Output per period

Unit Costs

MC

ATC

MC rises as production expands in the short run

ATC falls and then rises as production expands in the short runMC cuts ATC at

the minimum point on the ATC curve

Long Run vs Short Run Decisions

The Inflexibility of Short-Run Production

When a firm operates in the short run, its cost of production may not be minimized because of inflexibility in the use of capital inputs.

Output is initially at level q1, (using L1, K1).

In the short run, output q2can be produced only by increasing labor from L1 to L3 because capital is fixed at K1.

In the long run, the same output can be produced more cheaply by increasing labor from L1 to L2 and capital from K1 to K2.

Long Run vs Short-Run Cost Curves

The Relationship Between Short-Run and Long-Run Cost

The long-run average cost curve LAC is the envelope of the short-run average cost curves SAC1, SAC2, and SAC3.

With economies and diseconomies of scale, the minimum points of the short-run average cost curves do not lie on the long-run average cost curve.

If the firm knows how much output it can sell at any given price it can calculate total revenue, average revenue and marginal revenue at any output level

If the firms knows what its costs conditions would be at any output level it can calculate total cost, average cost and marginal cost

Armed with this revenue and cost information, the firm should be able to determine the production level; at which it would maximise profits

In practice, the outcome of this decision-making process depends on the nature of market conditions, which determine whether the firm is a price taker or a price setter


Profits and Production Again

54

End of Session 4

Documents

Business Economics Sessions 3 & 4