bm costs new

8/13/2019 BM Costs New

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Costs


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Production function gives technically feasible combinations of

inputs- Isoquants

*Isocost functions: Opportunity set

wL + rK = Tentative Budget

Production function and isocost functions are superimposed

and solved for arriving at the optimal combination.


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Point of tangency

Mathematically, slopes are equal

Equating the slopes we can solve for L and k


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Work out one example.


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Data requirements

Output levels, levels of inputs and their prices

These are the data require to arrive at Cost

functions


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An Example

An Example:

Short run production fn:Q = 5*60 0.5L 0.5

Q = 5 60L

Q2 = 1500L

L = Q2/1500; K = 60

R=5 w=10


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Short run cost figures for different Qs:

Q L K FC VC TC

0 0 60 300 0 300

100 6.67 300 66.7 366.67

200 26.67 300 266.7 566.7


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Short Run Cost Fn

How will it look?

What will it reflect?


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Short run cost Fn

It will reflect the behaviour of the MP of the

variable inputs.

That is eventually diminishing MP.


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Graphical representation

Var input

MP MC


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SR Total cost

TC

Q of output


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Long run total cost fn

How does returns to scale affect total costs?

Therefore, how does it affect average cost?

And so, how does it affect Marginal cost?


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Costs are Economic

Valuing a resource based on:

Opportunity cost - economic cost whenthere is no explicit cash outflow ; NO

economic cost when there is a cash outflow!!

The concept of relevant cost

In the long run, there is no such thing as a

free lunch.


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Long run

In the long run, scale expansion can lead to:

- returns to scale

- change in the process resulting in varying

input proportions

- change in input prices because of buyer

power due to large scale


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Long run in the context of costs

All these impact costs:

Economies and diseconomies of scale


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Long run cost functions

Longrun cost functions are similar but NO fixedfactor input. The fixed factor is interpreted as

technology.

Estimated empirically.

Cubic form to accommodate economies of scale in

the long run and diminishing returns in the short run.

Eg: TC= 200 +5Q -0.04Q2+ 0.001Q3


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Family of cost functions

Average Total Cost

Average Fixed Cost

Average Variable Cost Marginal cost


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Shapes of this?

Reflects the corresponding Production function.

Increasing returns corresponds to deceasing cost

Decreasing returns corresponds to increasing cost.

* A cubic fn captures both the phases.


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Mathematically, Marginal Cost(MC) is the derivative of TC

dTC/dQ is therefore the Marginal Cost.

Given TC function, we can get the MC Fn.

In the example,Given TC=200+5Q-.04Q2+0.001Q3,

MC=dTC/dQ=5-0.08Q+0.003Q2

AC=TC/Q=200/Q+5-0.04Q+0.001Q2


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We can derive AVC and AFC also

Min of the AC can also be derived as

dAC/dQ =0

This will give us that level of output at which

AC is MINIMUM.


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A problem

A Problem:

Given TC=100,000Q-1000Q

2

+10Q

3

A firm is planning to enter with a capacity of25 million.Given that the going price is

Rs.75000 per million and that the sellercannot change this price, should he goahead?


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Solution:

AC= 100000-1000Q+10Q2

dAC/dQ=-1000+20Q=0

20Q=1000

Q=50 mill

At 50 mill , AC=75,000 which is equal to the price. The firm should set up a capacity of 50 million.


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Economies of scope

C(q1,q2) < c(q1)+c(q2)

Index:((C(q1)+C(q2)- C(q1,q2))/C(q1,q2)


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Measurement of economies of scale

Cost-output elasticity?


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Profits

*Profit is max where the difference between TR and

TC is MAX.

This is at the level of Q*

*At Q* slopes of TC and TR are equal.

* Same as saying MC is equal to MR


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With MC and MR(in the first set of ppts) we

can define profit maximizing output as:

That level of output at which MC=MR


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Profit maximization

Is this condition sufficient?


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Second order condition:That point beyond

which MC exceeds MR.

Third condition: Does the price cover the AC

at this optimal level?


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First order condition:

dTR/dq = dTC/dq which is MR = MCSecond order condition:

For a maximum is d2/ dq2


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Supply curve

Derivation: The context- Price taking firm

The Profit maximizing rule becomes:

MC = MR , since MR = P, becomesMC = P


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So at different Prices, MC = P happens atdifferent quantities.


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Supply curve is derived from the rising part of

the MC curve above the minimum Average

Cost.


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Market Supply curve

Aggregation of individual supply curves.

Thus the two forces interact to determine the

equilibrium price.


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What the equlibrium price will be depends on the

relative strengths of the players who constitute the forces of

demand and supply.

*The relative strengths of the players on the Supply side

depends on the kind of Market structure they are operating in.

That takes us on to Market structures.

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