1.6.1 Production and Costs

Question 1

What are the properties of a private sector firm?

Answer 1

• Assume they maximise profits, ignoring potential conflicts between managers and owners as well as non-profit motives

Question 2

What is profit

Answer 2

The difference between revenues and cost

Revenue = price x quantity - what firm earns selling product

Cost is what a firm pays for inputs

To maximise profits, firms produce efficiently as possible - occurs if it cannot produce more output for a given quantity of inputs, given existing technology

Question 3

What is a production function

Answer 3

Shows maximium amount of output produced from combination of inputs by firms
- Assumes labour and capital only inputs, q = f(L,K)

Firm can easily adjust inputs in long run than short run so only 1 can ajdust in short run - usually labour and capital fixed and so we put a line above the K

The output q is also known as the total product of labour - total amount given amont of labour produces holding the quantity of other inputs fixed

Question 4

What is MPL and APL

Answer 4

Marginal product of labour is additional output produced bhy an additional unit of labour holding all other factors constant

MPL = dQ/dL = df(L,K)/dL

Average product of labour is ratio of output to the amount of labour employed

APl = q/L

This is also called marginal/average physical product of labour

Question 5

How is the production function, APL and MPL illustrated?

Answer 5

Illustrated on page 17

Question 6

What happens to MPL and APL?

Answer 6

APL first rises then falls. Firms first gain from better utilisation of capital and specialisation
- Employment increases too much relative to capital to harder to difficult extra output out of more labour

Note that APL curve slopes upwards where MPL curve is above it, downward MPL below it and peaks were APL = MPL - this is because after where they meet the marginal product is falling

Question 7

What is the law of diminishing returns?

Answer 7

If a firm keeps increasing an input, holding other inputs and technology constant, the corresponding increases in output eventually start to fall

Mathematically, dMPl/dL < 0

The slope of the total product curve stops increasing and vecomes flatter again

The LDMR is an empirical regularity - the typical shape of production fucntions is in part due to the LDMR.

Question 8

What are the properties of a production function with two variables?

Answer 8

In long run all inputs varied
- Graphed L against K

Production function describes how much output produced from combination of inputs

An isoquant shows the combination of inputs producing a specific output level

e.g. q = L^1/2 * K^1/2, to produce 6 inputs L and K must satisfy when q = 6

Or, K = 36/L

Question 9

Properties of Isoquants

Answer 9

Similar to indifference curves:

(Illustrated page 17)

1. Farther from origin, greater output level
2. Do not cross
3. Slope downwards
4. Must be thin

These properties all follow from assumption of efficient production underlying production functions

One important difference is isoquants have cardinal properties - not just ordinal ones

The shape of an isoquant indicates how easily a firm can substitute between inputs - the ability to replace one input with another holding output constant

Question 10

What are the types of isoquant?

Answer 10

lllustrated page 18

Perfect substitutes - q = K + L

Fixed proportions e.g. q = min(K,L)

Convex e.g. L^0.5 * K^0.5

Question 11

What is the marginal rate of technical substitution?

Answer 11

Slope of an isoquant at a single point

It is the change in K / Change in L OR dK/dL

Question 12

What happens to MRTS as we move down along an isoquant?

Answer 12

As we move down:

• Increase in L, output rises by df(L,K)/dL x dL = MPl x dL
• Decrease K, output falls by df(L,K)/dK x dK = MPk x dK
• Output constant, so MPL x dL = MPk x dK

Therefore:

MRTS = dK/dL = -MPl/MPk

(Example on page 18)

Question 13

What do the slopes of isoquants indicate?

Answer 13

• Exhibit dimishing MRTS
• More labour, harder to replace remaining capital with labour

As we move down isoquant, MPL goes down, MPK goes up so MRTS = - MPL/MPK gets closer to 0

• NOTE similarity to indifference curves and MRS between goods

Question 14

What is MRTS for linear and fixed proportion production functions?

Answer 14

Linear (q=L+K): MRTS = -1

Fixed proportions (q=min(L,K)): MRTS not defined because no substitutions possible

Question 15

What is returns to scale?

Answer 15

How much output changes if a firm increases all inputs proportionately

Firms determine optimal size in the long run, measured by a degree of returns to scale

Question 16

When does a production function exhibit constant/decreasing returns to scale?

Answer 16

Constant: percentage increase in inputs followed by same increase in output

q = f(2L,2K) = 2f(L,K)

Decreasing: percentage increase in inputs followed by smaller percentage increase in output

q = f(2L,2K) < 2f(L,K)

Increasing if it is greater than - occurs due to specialisation in capital and labour

Question 17

What is the typical pattern?

Answer 17

Many production functions exhibit varying returns to scale as output increases

Typical pattern:
- Increasing at low level - specialisation, grow faster through equipment
- Decreasing at high levels - coordination and organisation - DofS
- Reflected in spacing of isoquants (illustrated page 18)