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Introductory Microeconomics (ES10001)

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### Introductory Microeconomics (ES10001)

Topic 3: Production and Costs

I. Introduction Assumed to be upward sloping

- 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

I. 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

II. 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

II. 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

II. Profit

- Formally, we define accounting profit as:
- where TCa = totalaccountingcosts. We define economic profit as:
- where TC = TCa + OC denotes total costs

II. Profit

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

II. 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.

II. 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

III. 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

III. The Production Decision

- If additional unit of qcontributes more to TR than TC, then the firm increase production by one unit of q
- If additional unit of qcontributes 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 ofq changesTR and TC by the same amount

III. The Production Decision Thus, two key factors: We will look at each of these factors in turn.

- Strategy:
- MR > MC=>Increase q
- MR < MC=>Decrease q
- MR = MC=>Optimal q (i.e. q*)

- Costs firm incurs in producing q
- Revenue firm earns from producing q

III. 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

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

- 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

IV. 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

IV. 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

V. Productive Efficiency We describe productive efficiency in:

- 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.

- Long Run: ‘Returns to Scale’
- Short Run: ‘Returns to a Factor’

VI. 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

VI. 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

VI. 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)

VI. 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

VI. 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!

VI. Returns to Scale

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

VI. 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
- i.e.

VI. 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’

VI. Returns to Scale

- Note the relationship between LMC and LAC:
q < qmes LMC < LAC

q = qmes LMC = LAC

q > qmes LMC > LAC

VI. Returns to Scale

- Thus:
LAC is falling if: LMC < LAC

LAC is flat if: LMC = LAC

LAC is rising if: LMC > LAC

VII. 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:

VII. 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

VII. 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)

VII. 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)

VII. Returns to a Factor

- Formally:
- Or:

VII. 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)

VIII. 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

VIII. 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

VIII. 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!

VIII. Long- & Short-Run Costs

- First, consider the production function
- We envisage this as a collection of all efficient productiontechniques
- Production Technique: Using particular combination of inputs (K, L) to produce output (q)
- Consider the following:

VIII. 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;

Figure 19: Production Techniques

K

fa (2K, 1L)

2q

4K

Production Technique A (CRS)

fb (1K, 2L)

1q

2K

2q

Production Technique B (CRS)

1K

1q

L

0

1L2L 4L

VIII. 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

Figure 20: Production Techniques

K

fa (2K, 1L)

2q

4K

2q

3K

fb (1K, 2L)

1q

2K

2q

1K

1q

L

0

1L2L 3L 4L

Figure 21: Production Techniques

K

fa (2K, 1L)

2q

4K

2q

3K

fb (1K, 2L)

1q

2K

2q

1K

1q

L

0

1L2L 3L 4L

VIII. 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

Figure 22: Production Techniques

K

fa (2K, 1L)

2q

4K

fab (1K, 1L)

2q

3K

fb (1K, 2L)

1q

2K

2q

1K

1q

L

0

1L2L 3L 4L

Figure 22: Production Techniques

K

fa (2K, 1L)

2q

4K

fab (1K, 1L)

2q

3K

fb (1K, 2L)

1q

4/3q

2K

2q

2/3q

1K

1q

L

0

1L2L 3L 4L

VIII. 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

Figure 23: Production Techniques

Isoquont Map (i)

K

fa (2K, 1L)

2q

4K

2q

3.5K

1.5q

3K

fb (1K, 2L)

1q

2K

2q

1K

1q

0.5K

0.5q

L

0

1L 1.5L2L 3L 4L

Figure 23: Production Techniques

Isoquont Map (ii)

K

fa (2K, 1L)

2q

4K

2q

3.5K

1.5q

3K

fb (1K, 2L)

1q

2K

2q

1K

1q

0.5K

0.5q

L

0

1L 1.5L2L 3L 4L

Figure 24: Production Techniques

Isoquont Map (iii)

K

fa (2K, 1L)

2q

4K

fb (1K, 2L)

1q

2K

2q

1K

1q

L

0

1L2L 4L

Figure 25: Production Techniques

Isoquont Map (iv)

K

fa (2K, 1L)

2q

4K

fb (1K, 2L)

1q

2K

2q

2q

1q

1K

1q

L

0

1L 2L 4L

Figure 26 Production Techniques

Isoquont Map (v)

K

fa (2K, 1L)

2q

4K

fb (1K, 2L)

1q

2K

2q

2q

1q

1K

1q

L

0

1L2L 4L

VIII. 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

VIII. 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

Figure 30: Production Techniques

Isoquont Map (vii)

K

fa (2K, 1L)

2q

fd (1K, 1L)

2q

fb (1K, 2L)

1q

2q

2q

1q

1q

1q

L

0

Figure 31: Production Techniques

Isoquont Map (viii)

K

fa (2K, 1L)

2q

fd (1K, 1L)

2q

fb (1K, 2L)

1q

2q

2q

1q

1q

1q

L

0

VIII. 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

VIII. 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 bothK and L inputs
- Thus:

VIII. Long- & Short-Run Costs

- CRS: q2 = 2q1
q3 = 3q1

- IRS: q2 > 2q1
q3 > 3q1

- DRS: q2 < 2q1
q3 < 3q1

VIII. 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

VIII. 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

VIII. 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

VIII. 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

VIII. 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:

VIII. Long- & Short-Run Costs

- Consider underlying marginal cost curves
- At q1,slopes of the SRTC and LRTC curve are equalsuch that SRMC = LRMC
- For all q < (>) q1, slope SRTC < (>) LRTC such that SRMC cuts LRMC from below and to the left of q1

VIII. 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)

VIII. 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

VIII. 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

VIII. Long- & Short-Run Costs

- Note the tangencies between the LRAC curve and the various SRAC curves
- Implication - SRAC will fallandrise more rapidly than LRAC as q contracts or expands

VIV. 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

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