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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
3. The Production Decision
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
3. The Production Decision
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.
3. The Production Decision
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
Figure 10: IRS Implies Decreasing LAC
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
Figure 13: IRS Implies Decreasing 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
7. Returns to a Factor
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:
7. Returns to a Factor
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
Figure 15: Returns to a Factor
7. Returns to a Factor
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)
7. Returns to a Factor
Formally:
Or:
STC SFC STVC
STC
q
SFC
q
STVC
q
SAC SAFC SAVC
SAVC SAC SAFC
7. Returns to a Factor
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
Figure 16: Returns to a Factor
c
0 q
SMC
SAVC
SAC
SAFC
Figure 17: Returns to a Factor
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
8. Long- & Short-Run Costs
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
8. Long- & Short-Run Costs
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!
8. Long- & Short-Run Costs
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:
8. Long- & Short-Run Costs
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
Figure 19: Production Techniques
4K
2K
fa (2K, 1L)
Production Technique A (CRS)
Production Technique B (CRS)
8. Long- & Short-Run Costs
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
Figure 20: Production Techniques
4K
2K
fa (2K, 1L)
2q
K
0 L
3K
1q
1q fb (1K, 2L)
2q
2q
1K
1L 2L 3L 4L
Figure 21: Production Techniques
4K
2K
fa (2K, 1L)
2q
8. Long- & Short-Run Costs
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
Figure 22: Production Techniques
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
Figure 22: Production Techniques
4K
2K
fa (2K, 1L)
2q
fab (1K, 1L)
4/3q
2/3q
8. Long- & Short-Run Costs
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
Figure 23: Production Techniques
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
Figure 23: Production Techniques
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
Figure 24: Production Techniques
Isoquont Map (iii)
4K
2K
fa (2K, 1L)
K
0 L
1q
1q fb (1K, 2L)
2q
2q
1K
1L 2L 4L
Figure 25: Production Techniques
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
Figure 27: Production Techniques
Isoquont Map (vi)
1q
2q
8. Long- & Short-Run Costs
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
Figure 28: Production Techniques
fa (2K, 1L)
1q
2q
1q
2q
8. Long- & Short-Run Costs
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
Figure 29: Production Techniques
fa (2K, 1L)
1q
2q
1q
2q
K
0 L
1q
1q
fd (1K, 1L)
fb (1K, 2L)
2q
2q
Figure 30: Production Techniques
Isoquont Map (vii)
fa (2K, 1L)
1q
2q
1q
2q
K
0 L
1q
1q
fd (1K, 1L)
fb (1K, 2L)
2q
2q
Figure 31: Production Techniques
Isoquont Map (viii)
fa (2K, 1L)
1q
2q
1q
2q
K
0 L
Figure 32: Production Techniques
Isoquont Map (viv)
1q
2q
8. Long- & Short-Run Costs
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
Figure 33: Production Techniques
Isoquont Map (x)
8. Long- & Short-Run Costs
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
8. Long- & Short-Run Costs
CRS: q2 = 2q1
q3 = 3q1
IRS: q2 > 2q1
q3 > 3q1
DRS: q2 < 2q1
q3 < 3q1
8. Long- & Short-Run Costs
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
Figure 35: Returns to a Factor
3q
1L 2L 3L
1K
3K
2KA B C
A’
C’
A
8. Long- & Short-Run Costs
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
8. Long- & Short-Run Costs
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
8. Long- & Short-Run Costs
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
8. Long- & Short-Run Costs
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
Figure 38: LRTC and SRTC
STC(K*)
q1
E1
8. Long- & Short-Run Costs
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
8. Long- & Short-Run Costs
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
8. Long- & Short-Run Costs
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
Figure 37: LRTC and SRTC
c1c0
K0
K1
A
8. Long- & Short-Run Costs
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
Figure 39: LRAC Envelopes the SRAC
qmes
8. Long- & Short-Run Costs
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
Figure 40: LRAC Envelopes the SRAC
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