4 production and cost

EC2204- Business Economics4: Production and CostEC2204- Business Economics4: Production and Cost

Learning Outcomes

Upon completing this section, the student should be able to:

Define and understand the theory of production. Describe and illustrate a production function. Appreciate the meaning and measurement of cost. Differentiate between the various measures of cost. Distinguish between technical and economic

efficiency. Appreciate the concept of a Cobb-Douglas

production function Describe and illustrate the three stages of

production.

4: Production and Cost

In business economics we must decide not only what to produce for the market, but also how to produce it in the most efficient or least cost manner.

This section develops a widely accepted tool for judging whether or not the production choices are least cost.

A production function relates the most that can be produced from a given set of inputs.

This allows the manager to measure the marginal product of each input. In the short-run, some inputs are fixed.

The Law of Diminishing Marginal Returns applies to the short-run when some inputs are fixed.

The long-run production function deals with a period of time over which all inputs can vary.

Scale economies apply to the long-run case where all inputs can be varied.

Also, this section discusses reasons for increasing or decreasing returns in the long-run.

Production Functions in the Short-run

1. Each good or service produced requires inputs of time, materials, and capital. These resource inputs produce an output. If we listed the greatest output possible for any set of inputs, we would have described a production schedule, table, or function.

2. A production function is a schedule of maximum output from any set of inputs, Xi. Q = f (X1,X2,...,Xn)

3. Production is real. It is visible either in a large scale factory assembly line or in smaller scale in an artist's workshop. Production can be measured in the number of cars assembled or the number of paintings completed.

4. Yet even in something as real as production, it is vital to a manager to have methods to measure efficiency and ways to think about improving the production process. Theory is useful when it helps organize thought in constructive ways.

5. In economics, efficiency generally refers to the least cost way to do an activity.

6. A production function with two inputs: Q =f(K, L), where K is the amount of capital, and L is the amount of labor is used to illustrate issues in production.

7. A Cobb-Douglas Production Function relies on a multiplicative production model:

……… Cobb-Douglas Production Function

21 BLAKQ

Output (Q)

0 1 2 3 4 5 6 7 Units

1211

9

7

5

This point, at Q = 5, is both technically and economically

efficient(see Figure 7.2)

Total Product Curve

Production Function, Q = f (L, K)Law of Diminishing Returns

Increases in one factor of production such as, holding one or other factors fixed such as capital and entrepreneurship, after some point, lead to diminishing marginal increases in total product. i.e. the marginal product diminishes.

Economic EfficiencyOccurs at only one point – At the Level of output where MR = MC

Price

Output Q0 1 2 3 4 5 6 7 8

MC

P = D = MR = AR = MC

P

Economic efficiency occurs at 5 units of output only

MR = MC

Output (Q)

0 1 2 3 4 5 6 7 Units

1211

9

7

5

This point, at Q = 5, is both technically and economically

efficient(see Figure 7.2)

Total Product Curve

Production Function, Q = f (L, K)Law of Diminishing Returns

Increases in one factor of production such as, holding one or other factors fixed such as capital and entrepreneurship, after some point, lead to diminishing marginal increases in total product. i.e. the marginal product diminishes.

Cost Structure of a Firm (p60-61)

1 2 3 4 5 6 7 8 Output

(Q) FC VC TC AFC AVC ATC MC

(2+3) (2/1) (3/1) (4/1) ΔTC 1 30 40 70 30.0 40.0 70.0 - 2 30 60 90 15.0 30.0 45.0 20 3 30 90 120 10.0 30.0 40.0 30 4 30 130 160 7.5 32.5 40.0 40 5 30 180 210 6.0 36.0 42.0 50 6 30 250 280 5.0 41.7 46.7 70 7 30 350 380 4.3 50.0 54.3 100

Relationship between the Cost Curves

1. When the marginal cost is below the average cost (MC < AC), your average costs are falling.

2. When the marginal cost is equal to the average cost (MC = AC), your average cost stays the same.

3. When the marginal cost is above the average cost (MC > AC), your average costs are rising.

Note: MC curve always cut both the AVC and the ATC at their minimum points.

0

Cost’s /unit

Quantity (Q)

ATC

MC

AVC

Short-Run Average Cost Curves

0

Cost’s /unit

Quantity (Q)

ACFixed Costs are spread over a

larger output –Increasing returns to scale

Better use of specialisation

Law of Diminishing Returns set-in – Decreasing

returns to scale

Average Costs are minimized at point A

A

Long-Run Average Cost Curves

Long-Run Average Cost Curves are downward sloping due to:

1.Product-specific economies which include specialization and learning curve effects.

2.Plant-specific economies, such as economies in overhead, required reserves, investment, or interactions among products

3.Firm-specific economies which are economies in distribution and transportation of a geographically dispersed firm, or economies in marketing, sales promotion, or R&D of multi-product firms.

Economies of Scale: These include purchasing economies – a large firm can benefit from bulk purchases of inputs, construction economies – building costs do not increase with the size of the firm, economies – greater specialisation and division of – greater productivity, financial economies- better interest rate terms and advertising economies – advertising costs per unit of output are lower for a large firm.



Envelope of Short-Run ATC CurvesLong-Run Average Cost Curves are upward sloping due to:

1. Diseconomies of scale, examples include transportation costs, imperfections in the market, and problems of coordination and control by management.

2. The minimum efficient scale (MES) is the smallest scale at which minimum per unit costs are attained.

3. Modern business management offers techniques to avoid diseconomies of scale through profit centers, transfer pricing, and tying incentives to performance.

Diseconomies of Scale: These include managerial diseconomies – the bigger the firm the more difficult it is to manage, principal agent – conflict of interest between management and workers. (P/A problem), diseconomies – large companies have a higher proportion of ‘non-productive’ workers and infrastructure diseconomies- as the firm gets bigger greater demands are made on the infrastructure

Long-Run Average Cost Curve: the flat section is due to constant returns to scale.

The Three Stages of Production

Stage 1: The average product (AP) is rising where the AP is total output divided by number inputs (workers).

Stage 2: The average product is declining (but the marginal product (MP) is positive) where MP is the additional output generated from hiring one additional worker

Stage 3: The marginal product is negative, or total product (TP) is declining.

Sample Exam Question: Describe and illustrate the three stages of production.

Relationship between Inputs and Output

Production Functions and Returns to Scale

1. Constant Returns to Scale (CRS) increasing all inputs by lambda (λ) percent, increases output by lambda percent.

2. Increasing Returns to Scale (IRS)--increasing all inputs by lambda percent, increases output by more than lambda percent.

3. Decreasing Returns to Scale (DRS)--increasing all inputs by lambda percent, does not quite increase output by lambda percent.

4. A production function Q = f(x, y) is homogeneous of degree n, if:f(λx, λy) = λn f (x, y) for λ ≠ 0.

5. A Cobb-Douglas production function: Q = A Kα Lβ- can be IRS, CRS, or DRS. This function is homogeneous of degree = α + β

Production Functions and Returns to Scale

5. A Cobb-Douglas production function: Q = A Kα Lβ- can be IRS, CRS, or DRS. This function is homogeneous of degree = α + β.

a. If α + β = 1 then your production function is Constant Returns to Scale (CRS).

b. If α + β > 1 then your production function is Increasing Returns to Scale (IRS).

c. If α + β < 1 then your production function is Decreasing Returns to Scale (DRS).

A Cobb-Douglas production function: Q = A K0.6 L0.4

This function is Constant Returns to Scale (CRS) as α + β = 1 (0.6 + 0.4 = 1.0)


The function is Increasing Returns to Scale (IRS) as α + β > 1 (0.6 + 0.5 = 1.1)


The function is Decreasing Returns to Scale (DRS) as α + β < 1(0.4 + 0.5 = 0.9)

Cobb-Douglas Production Functions

The generalized Cobb-Douglas production function Q = A Kα Lβ is linear in logs

Log Q = Log A + α Log K + β Log L

Log Q = Log A + 0.6 Log K + 0.4 Log L – CRS Log Q = Log A + 0.6 Log K + 0.5 Log L – IRS Log Q = Log A + 0.4 Log K + 0.5 Log L – DRS

where α is the capital elasticity of output, α = EK and β is the labour elasticity of output, β = EL

Sample Question 1

Let there be a cubic VC function: VC = 0.5Q3 - 10Q2 + 150Q

1. Find AVC from VC function?2. Find minimum average variable cost of output?3. Find MC function from VC function?

Minimum AVC, is where 1.where AVC = = 0.5Q2 -

10Q + 150

2. = Q -10 = 0, So Q = 10, AVC minimised at Q =10

3. MC function =

0

Q

AVC

Q

VC

Q

QQQ 150105.0 23

Q

AVC

150205.1 2

QQQ

TC

Sample Question 2Consider the following variable cost function: VC = 120Q - 9Q2 +

0.25Q3. Fixed costs = 180 and Q = output.a. Determine the average variable cost (AVC) function? AVC = = = 120Q – 9Q

+0.25Q2

b. Find the level of output Q that minimises average variable costs?

AVC are minimised when -9 + 0.5Q = 0, so Q = 4.5

c. Determine the marginal cost (MC) function?Recall TC = FC + VC, so TC = 180 + 120Q - 9Q2 + 0.25Q3.

MC function =

Q

VC

Q

QQQ 32 25.09120

0Q

VC

275.018120 QQQ

TC

Sample Question 3

Suppose: Q = 1.4 L0.70 K0.35

Q1. Is this function homogeneous? A. It’s homogeneous to degree 1.05

Q2. Is the production function constant returns to scale? A. No. it’s IRS as increases in all inputs by λ, increase output by 1.05

Q3. What is the elasticity of output? A. Elasticity of output is 0.70Q4. What is the capital elasticity of output? A. Capital elasticity of

output is 0.35Q5. What happens to Output (Q), if (L) increases by 3% and capital

(K) is cut 10%? - Ans.- %ΔQ = 0.70*3% + 0.35* -10% = 2.1% - 3.5% = -1.4%

Conclusion: Output (Q) drops by 1.4%

Sample Question 4Output (Q) Fixed Cost (€) Variable Cost (€)

0 50 0 5 50 20 10 50 35 15 50 55 20 50 80

Use the above table to answer the following questionsa. Calculate the average total cost (ATC) at output = 20 ATC = = = €6.50 Q

TCQ

VCFC

20

8050

b. At output = 10, what is the TC?

TC = FC + VC = 50 + 35 = 85

c. What is the Marginal Cost (MC) as output is increased from 5 to 10 units?

As output is increased from 5 to 10 units, ΔTC = [ΔFC= 0 + ΔVC=15] and ΔQ = 5

So MC = = €35

15

Q

TC

MCQ’s

You are given the following cost function: TC = 1,500 + 300Q + 25Q2. From this cost we know:

a. Fixed cost is 300. b. Average total cost is 1500/Q. c. Total cost declines as Q rises, d. Marginal cost is 300 + 50Q

4. If marginal costs are greater than average total costs, then:

a. average total cost curve is falling, b. average total cost curve is flat, c. average total cost curve is rising, d. average total cost curve is a minimum.

Recall our Learning Outcomes

You should now be able to:

Define and understand the theory of production. Describe and illustrate a production function. Appreciate the meaning and measurement of

cost. Differentiate between the various measures of

cost. Distinguish between technical and economic

efficiency. Appreciate the concept of a Cobb-Douglas

production function Describe and illustrate the three stages of

production.

4 production and cost

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