Introductory Microeconomics (ES10001) Topic 4: Production and Costs.

Introductory Microeconomics (ES10001)

Topic 4: Production and Costs

1. Introduction

We now begin to look behind the Supply Curve

Recall: Supply curve tells us:

• Quantity sellers willing to supply at particular price per unit;

• Minimum price per unit sellers willing to sell particular quantity

Assumed to be upward sloping

1. Introduction

We assume sellers are owner-managed firms (i.e. no agency issues)

Firms objective is to maximise profits

Thus, supply decision must reflect profit-maximising considerations

Thus to understand supply decision, we need to understand profit and profit maximisation

Revenue Costs of Productionq*

‘Optimal’ Output

Figure 1: Optimal Output

2. Profit

Profit = Total Revenue (TR) - Total Costs (TC)

Note the important distinction between Economic Profit and Accounting Profit

Opportunity Cost (OC) - amount lost by not using a particular resource in its next best alternative use.

Accountants ignore OC - only measure monetary costs

2. Profit

Example: self-employed builder earns £10 and incurs £3 costs; his accounting profit is thus £7

But if he had the alternative of working in MacDonalds for £8, then self-employment ‘costs’ him £1 per period.

Thus, it would irrational for him to continue working as a builder

2. Profit

Formally, we define accounting profit as:

where TCa = total accounting costs. We define economic profit as:

where TC = TCa + OC denotes total costs

a TR TC a

TR TC

2. Profit

Thus:

Thus, economists include OC in their (stricter) definition of profits

TR TC TR TC a OC

TR TC a OC

a OC

2. Profit

Define Normal (Economic) Profit

That is, where accounting profit just covers OC such that the firm is doing just as well as its next best alternative.

a OC 0

a OC

2. Profit

Define Super-normal (Economic) Profit:

Supernormal profit thus provides true economic indicator of how well owners are doing by tying their money up in the business

a OC 0

a OC

3. The Production Decision

Optimal (i.e. profit-maximising) q (i.e. q*) depends on marginal revenue (MR) and marginal cost (MC)

Define: MR = ΔTR / Δq

MR = ΔTC / Δq

Decision to produce additional (i.e. marginal) unit of q (i.e. Δq = 1) depends on how this unit impacts upon firm’s total revenue and total costs


If additional unit of q contributes more to TR than TC, then the firm increase production by one unit of q

If additional unit of q contributes less to TR than TC, then the firm decreases production by one unit of q

Optimal (i.e. profit maximising) q (i.e. q*) is where additional unit of q changes TR and TC by the same amount


Strategy:• MR > MC => Increase q

• MR < MC => Decrease q

• MR = MC => Optimal q (i.e. q*)

Thus, two key factors:• Costs firm incurs in producing q

• Revenue firm earns from producing q

We will look at each of these factors in turn.


Revenue affected by factors external to the firm. essentially, the environment within which it operates

Is it the only seller of a particular good, or is it one of many? Does it face a single rival?

We will explore the environments of perfect competition, monopoly and imperfect competition

But first, we explore costs

4. Costs

If the firm wishes to maximise profits, then it will also wish to minimise costs.

Two key factors determine costs of production:• Cost of productive inputs

• Productive efficiency of firm

i.e. how much firm pays for its inputs; and the efficiency with which it transforms these inputs into outputs.

4. Costs

Formally, we envisage the firm as a production function:

q = f(K, L)

Firm employs inputs of, e.g., capital (K) and labour (L) to produce output (q)

Assume cost per unit of capital is r and cost per unit of labour is w

K

L

q = f(K, L)

Figure 2: The Firm as a Production Function

Inputs Output

r

w

4. Costs

Assume for simplicity that the unit cost of inputs are exogenous to the firm

Thus, it can employ as many units of K and L it wishes at a constant price per unit

To be sure, if w = £5, then one unit of L would cost £5 and 6 units of L would cost £30

Consider, then, productive efficiency

5. Productive Efficiency

We describe efficiency of the firm’s productive relationship in two ways depending on the time scale involved:

• Long Run: Period of time over which firm can change all of its factor inputs

• Short Run: Period of time over which at least one of its factor is fixed.

We describe productive efficiency in:• Long Run: ‘Returns to Scale’

• Short Run: ‘Returns to a Factor’

6. Returns to Scale

Describes the effect on q when all inputs are changed proportionately

e.g. double (K, L); triple (K, L); increase (K, L), by factor of 1.7888452

Does not matter how much we increase capital and labour as long as we increase them in the same proportion

6. Returns to Scale

Increasing Returns to Scale: Equi-proportionate increase in all inputs leads to a more than equi-proportionate increase in q

Decreasing Returns to Scale: Equi-proportionate increase in all inputs leads to a less than equi-proportionate increase in q

Constant Returns to Scale: Equi-proportionate increase in all inputs leads to same equi-proportionate increase in q

6. Returns to Scale

What causes changes in returns to scale?

Economies of Scale: Indivisibilities; specialisation; large Scale / better machinery

Diseconomies of Scale: Managerial diseconomies of Scale; geographical diseconomies

Balance of two forces is an empirical phenomenon (see Begg et al, pp. 111-113)

6. Returns to Scale

How do returns to scale relate to firm’s long run costs?

Efficiency with which firm can transform inputs into output in the long run will affect the cost of producing output in the long run

And this, will affect the shape of the firms long run total cost curve

c

0 q

LTC

10 20 30

5

10

15

Figure 3: LTC & Constant Returns to Scale

c

0 q

LTC

10 20 30

5

12

25

Figure 4: LTC & Decreasing Returns to Scale

c

0 q

LTC

10 20 30

5

8

10

Figure 5: LTC & Increasing Returns to Scale

6. Returns to Scale

LTC tells firm much profit is being made given TR; but firm wants to know how much to produce for maximum profit.

For this it needs to know MR and MC

So can LTC tell us anything about LMC?

Yes!

6. Returns to Scale

Slope of line drawn tangent to LTC curve at particular level of q gives LMC of producing that level of q

1.e. LMC

ΔLTC

Δq

c

0 q

LTC

q0 q1

01 qqq Δ

ΔLTC c q1 c q

0

x c q

0

c q1

Figure 6a: LTC & LMC

Tan x = ΔLTC / Δq

c

0 q

LTC

q0 q1

Δq q1 q

0

ΔLTC c q1 c q

0 x

c q0

c q1

Figure 6b: LTC & LMC

Tan x = ΔLTC / Δq

c

0 q

LTC

q0 q1

Δq q1 q

0

ΔLTC c q

1 c q0

x c q

0 c q

1

Figure 6c: LTC & LMC

Tan x = ΔLTC / Δq

c

0 q

LTC

c q0

Figure 6d: LTC & LMC

Tan x = LMC(q0)

q0

x

c

0 q

LTC

c q0

Figure 6e: IRS Implies Decreasing LMC

q0 q1

c q1

c

0 q

LMC

LMC q0

Figure 7: IRS Implies Decreasing LMC

q0 q1

LMC q1

6. Returns to Scale

Similarly, slope of line drawn from origin to point on LTC curve at particular level of q gives LAC of producing that level of q

1.e. LAC

LTC

q

c

0 q

LTC

q0

x

c q0

c q0

q0

Figure 8: LTC & LAC

Tan x = LAC(q0)

c

0 q

LTC

z

Figure 9: IRS Implies Decreasing LAC

Tan x = LAC(q0)

x

c

0 q

LAC

LAC q0


q0 q1

LAC q1

6. Returns to Scale

Generally, we will assume that firms first enjoy increasing returns to scale (IRS) and then decreasing returns to scale (DRS)

Thus, there is an implied ‘efficient’ size of a firm

i.e. when it has exhausted all its IRS

qmes - ‘minimum efficient scale’

c

0 q

LTC

Figure 11: IRS and then DRS

qmes

6. Returns to Scale

Note the relationship between LMC and LAC:

q < qmes LMC < LAC

q = qmes LMC = LAC

q > qmes LMC > LAC

c

0 q

LTC

Figure 12a: IRS and then DRS

LMC < LAC

c

0 q

LTC

Figure 12b: IRS and then DRS

LMC < LACLAC =LMC

c

0 q

LTC

Figure 12c: IRS and then DRS

LMC < LACLAC =LMC

LMC > LAC

c

0 q

LTC

Figure 12d: IRS and then DRS

LAC > LMCLAC =LMC

LMC > LAC

qmes

6. Returns to Scale

Thus:

LAC is falling if: LMC < LAC

LAC is flat if: LMC = LAC

LAC is rising if: LMC > LAC

c

0 q

LTC

q0

qmes

LMC

LAC


7. Returns to a Factor

Returns to a factor describe productive efficiency in the short run when at least one factor is fixed

Usually assumed to be capital

Short-run production function:

q f K , L


Increasing Returns to a Factor: Increase in variable factor leads to a more than proportionate increase in q

Decreasing Returns to a Factor: Increase in variable factor leads to a less than proportionate increase in q

Constant Returns to a Factor: Increase in variable factor leads to same proportionate increase in q

q

0 L

CRF

DRF

IRF

Figure 14: Returns to a Factor

q f K , L Short-Run Production Function:


Implications for short-run total cost curve

Constant returns to a factor implies we can double q by doubling L; if unit price of L is constant, this implies a doubling of cost

Similarly, if returns to a factor are increasing (i.e. less than doubling of costs) or decreasing (more than doubling of costs)

c

0 q

SRTCCRF

SRTCIRF

SRTCDRF

TFC



Fixed and Variable Costs

Since in the short run at least one factor is fixed, the costs associated with that factor will also be fixed and so will not vary with output

Thus, in the short run, costs are either: • Fixed: Do not vary with q (e.g. rent)

• Variable: Vary with q (e.g. energy, wages)


Formally:

Or:

STC SFC STVC

STC

q

SFC

q

STVC

q

SAC SAFC SAVC

SAVC SAC SAFC


The ‘Law of Diminishing Returns’

Whatever we assume about the returns to scale characteristics of a production function, it is always that case that decreasing returns to a factor (i.e. diminishing returns) will eventually set in

Intuitively, it becomes increasingly difficult to raise q by adding increasing quantities of a variable input (e.g. L) to a fixed quantity of the other input (e.g. K)

c

0 q

STVC

STC

SFC


c

0 q

SMC

SAVC

SAC

SAFC


8. Long- & Short-Run Costs

What is the relationship between long-run and short-run costs?

The latter are derived for a particular level of the fixed input (i.e. capital)

We can examine the relationship via the tools we developed in our study of consumer theory


We envisage the firm as choosing to maximise its output subject to a cost constraint

or:

Minimising its costs subject to an output constraint

N.B. Assumption of competitive markets


Formally:

Max q = f(K, L) s.t c = wL + rK = c0

or:

Min c = wL + rK s.t q = f(K, L) = q0

N.B. Duality!


First, consider the production function

We envisage this as a collection of all efficient production techniques

Production Technique: Using particular combination of inputs (K, L) to produce output (q)

Consider the following:


Assume firm has two production techniques (A, B) both of which exhibit CRS

Technique A requires 2 units of K and 1 unit of L to produce 1 unit of q

Technique B requires 1 unit of K and 2 units of L to produce 1 unit of q;

K

0 L

1q

2q

1L 2L

Figure 18: Production Techniques

4K

2K

fa (2K, 1L)

Production Technique A (CRS)

K

0 L

1q

1q fb (1K, 2L)

2q

2q

1K

1L 2L 4L


4K

2K

fa (2K, 1L)

Production Technique A (CRS)

Production Technique B (CRS)


We assume that firm can combine the two techniques

For example, produce 1 unit of q via Production Technique A and 1 unit of q via Production Technique B

K

0 L

3K

1q

1q fb (1K, 2L)

2q

2q

1K

1L 2L 3L 4L


4K

2K

fa (2K, 1L)

2q


By combining techniques A and B in this way, the firm has effectively created a third technique

i.e. Technique ‘AB’

Technique AB requires 1.5 unit of K and 1.5 unit of L to produce 1 unit of q

K

0 L

3K

1q

1q fb (1K, 2L)

2q

2q

1K

1L 2L 3L 4L


4K

2K

fa (2K, 1L)

2q

fab (1K, 1L)

K

0 L

3K

1q

1q fb (1K, 2L)

2q

2q

1K

1L 2L 3L 4L


4K

2K

fa (2K, 1L)

2q

fab (1K, 1L)

4/3q

2/3q


If the firm is able to combine the two production techniques in any proportion, then it will be able to produce 2 units of q (or indeed, any level of q) by any combination of K and L

We can thus begin to derive the firm’s isoquont map

Isoquont: Line depicting combinations of K and L that yield the same level of q

K

0 L

1q

1q fb (1K, 2L)

2q

2q

1K

1L 1.5L 2L 3L 4L


Isoquont Map (i)

4K

2K

fa (2K, 1L)

2q

3K1.5q

3.5K

0.5K 0.5q

K

0 L

1q

1q fb (1K, 2L)

2q

2q

1K

1L 1.5L 2L 3L 4L


Isoquont Map (ii)

4K

2K

fa (2K, 1L)

2q

3K1.5q

3.5K

0.5K 0.5q

K

0 L

1q

1q fb (1K, 2L)

2q

2q

1K

1L 2L 4L


Isoquont Map (iii)

4K

2K

fa (2K, 1L)

K

0 L

1q

1q fb (1K, 2L)

2q

2q

1K

1L 2L 4L


Isoquont Map (iv)

4K

2K

fa (2K, 1L)

1q

2q

K

0 L

1q

1q fb (1K, 2L)

2q

2q

1K

1L 2L 4L

Figure 26 Production Techniques

Isoquont Map (v)

4K

2K

fa (2K, 1L)

1q

2q

K

0 L


Isoquont Map (vi)

1q

2q


Consider discovery of production technique C

Technique C also exhibits CRS

But Technique C requires more inputs than Technique AB to produce q

It is therefore technically inefficient and would not be adopted by a profit maximising firm

K

0 L

1q

1q

fc (1K, 1L)

fb (1K, 2L)

2q

2q


fa (2K, 1L)

1q

2q

1q

2q


Only technically efficient production techniques (such as Technique D) would be adopted

Thus, the firm’s isoquont will never be concave towards the origin and will in general be convex

K

0 L

1q

1q

fd (1K, 1L)

fb (1K, 2L)

2q

2q


fa (2K, 1L)

1q

2q

1q

2q

K

0 L

1q

1q

fd (1K, 1L)

fb (1K, 2L)

2q

2q


Isoquont Map (vii)

fa (2K, 1L)

1q

2q

1q

2q

K

0 L

1q

1q

fd (1K, 1L)

fb (1K, 2L)

2q

2q


Isoquont Map (viii)

fa (2K, 1L)

1q

2q

1q

2q

K

0 L


Isoquont Map (viv)

1q

2q


The more technically efficient techniques there are, each using K and L in different proportions, then the more kinks there will be in the isoquont and the more it will come to resemble a smooth curve, convex to the origin

Analogous to consumer’s indifference curve

K

0 L

q0

q1


Isoquont Map (x)


We can measure the firms Returns to Scale in terms of isoquonts by moving along a ray from the origin

i.e. returns to scale implies that firm is in the long run and can change both K and L inputs

Thus:

K

0 L

q1

q2

Figure 34: Returns to Scale

q3

1L 2L 3L

1K

3K

2K

A


CRS: q2 = 2q1

q3 = 3q1

IRS: q2 > 2q1

q3 > 3q1

DRS: q2 < 2q1

q3 < 3q1


We can measure the firm’s Returns to a Factor (i.e. K) by moving along a horizontal line from the particular level of K being held fixed

Note that firm will always incur decreasing returns to a factor, irrespective of its returns to scale

In what follows, we have CRS but DRF - successively larger increases in L are required to yield proportionate increases in q

K

0 L

1q

2q


3q

1L 2L 3L

1K

3K

2KA B C

A’

C’

A


Analogous to consumer’s budget constraint, we can also derive the firm’s isocost curve

Isocost curve: line depicting equal cost expended on inputs

c = rK + wL

Firm’s optimal choice - tangency condition


Recall - firm’s problem:

Max q = f(K, L) s.t c = wL + rK = c0

or:

Min c = wL + rK s.t q = f(K, L) = q0

K

0 L

q1

c1/w

c1/r

Figure 36: Optimal Input Decision

E1

L1

K1


Consider SR / LR cost of producing q

SR cost (say, when K = K1) is higher than LR cost except for one particular level of q

In the following example, c1 is minimum cost of producing q1 in both SR and LR

Rationale? Given (r, w), K1 is optimum (i.e. cost-minimising) level of K with which to produce q1

K

0 L

q0

q1

Figure 37: LRTC and SRTC

q2

E0 E1 E2

c2

c1

c0

K1

A


Thus, for every level of q ≠ q1, short-run costs exceed long-run costs

Assuming increasing returns and then decreasing returns to both scale and to a factor, it must be the case that the short-run total cost curve (for a particular level of K) lays above the long-run total cost curve except at one particular level of output

Thus:

c

0 q

LTC


STC(K*)

q1

E1


Consider underlying marginal cost curves

At q1, slopes of the SRTC and LRTC curve are equal such that SRMC = LRMC

For all q < (>) q1, slope SRTC < (>) LRTC such that SRMC cuts LRMC from below and to the left of q1


Now consider underling average cost curves

SRAC = LRAC at q1 whilst SRAC > LRAC for all q ≠ q1 such that SRAC and LRAC are tangent at q1

N.B. Tangency does not imply that SRAC is at a minimum at q1, only that SRAC will fall/rise more rapidly than LRAC as q expands/contracts (i.e. not implication that SRAC will rise in absolute terms)

c

0 q

LAC

SAC1

Figure 40: LRAC Envelopes the SRAC

q1

LMCSMC1


Now consider change in fixed level of capital

Recall - each short-run total cost curve is drawn for a specific level of fixed capital

As fixed level of K rises, level of q at which SRTC = LRTC also rises

K

0 L

q0

q1


c1c0

K0

K1

A


If both LRAC & SRAC are u-shaped, then it must be the case that the former is an envelope of the latter

c

0 q

LAC

SAC1

SAC2

SAC3

SAC4

SAC5 SAC6


qmes


Note the tangencies between the LRAC curve and the various SRAC curves

Implication - SRAC will fall and rise more rapidly than LRAC as q contracts or expands

c

0 q

LAC

SAC1 SAC3

SMC2


q1 q2 = qmes q3

LMCSMC1

SMC3

SAC2

V4. Final Comments

We now turn our attention to the revenue side of the firm’s profit maximising decision

We need to understand how revenue changes as we change output

i.e. Marginal Revenue (MR)

And how MR is determined by market environment within which the firm operates

Introductory Microeconomics (ES10001) Topic 4: Production and Costs.

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Transcript of Introductory Microeconomics (ES10001) Topic 4: Production and Costs.