Producer Theory

Question 1

How can a Production function be denoted as?

Answer 1

q = f(K,L)

Question 2

How can we define a Production Function?

Answer 2

It describes the maximum output, q, that a firm can produce efficiently with a given combination of capital and labour, {K, L}, conditional on the firm’s current
technology and organisation.

Question 3

What is the Short Run defined as?

Answer 3

Defined as the period in which a firm is unable to change the level of at least one factor of production.

• Generally capital (K bar) Bar is the line on top
• Could be labour (But not considered)

Question 4

What is the Short Run production function?

Answer 4

q = f (K bar, L).

Question 5

What is the Marginal Product of Labour?

Answer 5

MPL, is the increase in output that results
from an extra single unit of labour, holding all else constant.
- It is characterised by the gradient of the short run production function.

Question 6

How do we denote the MPL?

Answer 6

MPL = ∂q/∂L = ∂f(K bar, L)/∂L

Question 7

What is the Average Product of Labour?

Answer 7

APL, is the ratio of output to the number of

labour units employed.

Question 8

How do we denote the APL?

Answer 8

APL = q/L = f(K bar,L)/L

Question 9

How do we denote Fixed Costs in the Short Run?

Answer 9

Fixed Costs - F

Question 10

How do we denote Variable Costs in the Short Run?

Answer 10

VC(q)

Question 11

How do we denote Total Costs in the Short Run?

Answer 11

C(q) = F +VC(q)

Question 12

How do we denote Marginal Costs in the Short Run?

Answer 12

MC(q) = dC(q)/dq = dVC(q)/dq

Question 13

When does the Marginal Cost denotation change?

Answer 13

When capital is fixed in the SR and when wages, w, are constant, then
VC(q) = wL(q), where L(q) is the labour require to produce q units of output.

Question 14

What does the Marginal Cost change to when Capital is fixed in the SR and when wages are constant?

(USE THIS)

Answer 14

Then MC(q) =
 dVC(q)/dq = W dl/dq = w (1/dq/dl) = W(1/MPL) = w/MPL

So the marginal cost is w(1/MPL)

Question 15

Why is the Marginal Cost w(1/MPL)?

Answer 15

because of the following: MPL is the number of units of output generated from an extra unit of labour.
Therefore, to generate one extra unit of output, the firm needs (1/MPL) units of labour.

Question 16

How do we denotes Average Fixed Costs?

Answer 16

AFC(q) = F/q

Question 17

How do we denote Average Variable Costs?

Answer 17

AVC(q) = VC(q)/q

Question 18

How do we denote Average Costs?

Answer 18

AC(q) = C(q)/q = (F+VC(q))/q

= AFC +AVC

Question 19

What is the AFC dependant on?

Answer 19

The AFC is strictly falling with output

Question 20

Why is the Average Cost Curve U shaped?

Answer 20

Average variable costs may decrease with output but then begin to increase
with output for larger levels of output when diminishing marginal returns set in.

Question 21

What is the difference between the Long Run and the Short Run?

Answer 21

In the long run, firms are free to select any level of capital and labour. (To study this use Isoquants)

In short run Capital is fixed

Question 22

What do Isoquants describe?

Answer 22

Isoquants describe the possible combinations of factors (labour and capital) that, when used efficiently, generate a given level of output;
f (K, L) = q bar

-Often assumed to have similar properties and similar shape to Indifference Curves

SEE GRAPH IN NOTES

Question 23

What are the assumptions that the properties of Isoquants follow from?

Answer 23

The properties of isoquants follow from the assumptions that:

i) the firm uses the factors efficiently and that,
ii) the marginal product of both factors is always positive.

Question 24

What are the Properties of Isoquants?

Answer 24

• Output increases with distance from origin
• Isoquants cannot cross
• Isoquants are downward sloping
• Isoquants cannot be ‘thick’
• Isoquants are convex to the origin.

Question 25

What is the gradient of an Isoquant called?

Answer 25

Called the Marginal Rate of Technical Substitution (MRTS)

Question 26

What does the MRTS describe?

Answer 26

It describes the change in the units of capital required to keep output constant
following a unit increase in labour

Question 27

How can we calculate the MRTS?

Answer 27

MRTS =
-∂f (K,L)/∂L / ∂f(K,L)/∂k
= - MPL/MPK

Question 28

What happens if the Isoquant is convex to the origin?

Answer 28

Its MRTS is diminishing

Question 29

Why does the MRTS diminish when the Isoquant is convext to the origin?

Answer 29

Follows directly from the law of diminishing marginal returns.

For example, consider a point where L is high and K is low.

Here, the law implies that an additional unit of labour will generate only a relatively small amount of output (low MPL), which can be offset by a relatively small reduction
in capital (high MPK) to keep output constant. 

That is, the MRTS is relatively
flat. The opposite is then true for a point with low L and high K.

Question 30

What do Isocost Lines describe?

Answer 30

Describe the possible combinations of inputs that constitute a given total cost,
C bar

For a wage rate, w, and capital rental rate, r, an isocost line, can be described
by
C = wL + rK.

By rearranging, this gives
K = (C/r) – (w/r)L

SEE GRAPH IN NOTES

Question 31

How do we find Optimal Choice graphically?

Answer 31

• Pick the highest Isoquant given a Max Isocost line

-However, this is exactly the same as saying the firm would like to choose capital and labour in order to minimise costs subject to output being greater or
equal than some level. (Pick lowest isocost given a particular isoquant).

• Standard to think about a firm’s optimal choice of inputs as a cost minimisation problem rather than an output maximisation problem.

SEE DIAGRAM IN NOTES

Question 32

How do we find the Optimal Choice mathematically?

Answer 32

Via the lagrangian method

SEE EXAMPLE IN NOTES

Question 33

What are Conditional Factor Demand Functions?

Answer 33

-They describe the
firm’s demand for the factors conditional on producing a given level of output,
q.

L* = L* (w,r,q) and K* = K* (w,r,q)

Question 34

How can you calculate the Long Run Costs - LRTC?

Answer 34

Via Conditional factor demand functions, L(w, r, q) and K(w, r, q),

long run total costs can be
expressed as:
C(q) = w L(w, r, q) + r K(w, r, q)

Question 35

How do you calculate the Long Run Marginal Costs (LRMC)?

Answer 35

λ* = w(1/MPL) = r(1/MPK)
When evaluated at L,K

The λ* can be understood as LRMC

SEE EXAMPLE IN NOTES