Producer Theory Flashcards
How can a Production function be denoted as?
q = f(K,L)
How can we define a Production Function?
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.
What is the Short Run defined as?
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)
What is the Short Run production function?
q = f (K bar, L).
What is the Marginal Product of Labour?
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.
How do we denote the MPL?
MPL = ∂q/∂L = ∂f(K bar, L)/∂L
What is the Average Product of Labour?
APL, is the ratio of output to the number of
labour units employed.
How do we denote the APL?
APL = q/L = f(K bar,L)/L
How do we denote Fixed Costs in the Short Run?
Fixed Costs - F
How do we denote Variable Costs in the Short Run?
VC(q)
How do we denote Total Costs in the Short Run?
C(q) = F +VC(q)
How do we denote Marginal Costs in the Short Run?
MC(q) = dC(q)/dq = dVC(q)/dq
When does the Marginal Cost denotation change?
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.
What does the Marginal Cost change to when Capital is fixed in the SR and when wages are constant?
(USE THIS)
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)
Why is the Marginal Cost w(1/MPL)?
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.
How do we denotes Average Fixed Costs?
AFC(q) = F/q
How do we denote Average Variable Costs?
AVC(q) = VC(q)/q
How do we denote Average Costs?
AC(q) = C(q)/q = (F+VC(q))/q
= AFC +AVC
What is the AFC dependant on?
The AFC is strictly falling with output
Why is the Average Cost Curve U shaped?
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.
What is the difference between the Long Run and the Short Run?
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
What do Isoquants describe?
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
What are the assumptions that the properties of Isoquants follow from?
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.
What are the Properties of Isoquants?
- Output increases with distance from origin
- Isoquants cannot cross
- Isoquants are downward sloping
- Isoquants cannot be ‘thick’
- Isoquants are convex to the origin.
What is the gradient of an Isoquant called?
Called the Marginal Rate of Technical Substitution (MRTS)
What does the MRTS describe?
It describes the change in the units of capital required to keep output constant
following a unit increase in labour
How can we calculate the MRTS?
MRTS =
-∂f (K,L)/∂L / ∂f(K,L)/∂k
= - MPL/MPK
What happens if the Isoquant is convex to the origin?
Its MRTS is diminishing
Why does the MRTS diminish when the Isoquant is convext to the origin?
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.
What do Isocost Lines describe?
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
How do we find Optimal Choice graphically?
- 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
How do we find the Optimal Choice mathematically?
Via the lagrangian method
SEE EXAMPLE IN NOTES
What are Conditional Factor Demand Functions?
-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)
How can you calculate the Long Run Costs - LRTC?
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)
How do you calculate the Long Run Marginal Costs (LRMC)?
λ* = w(1/MPL) = r(1/MPK)
When evaluated at L,K
The λ* can be understood as LRMC
SEE EXAMPLE IN NOTES
