Managerial economics guide 8

AFC Y*

In the long run you will still have an U shape cost curve just because the fixed cost will always decrease and don’t change the shape of the total cost

():

Marginal cost cut average cost at the minimum of the average cost at its minimum value

If marginal cost is below average cost, the cost of one extra unit is less than average production cost, so the average cost curve will go down. The opposite

will happen when marginal cost is above average cost. These two will intercept at the peak or the minimum point of the AVC

From short run curve to long run curve

We have many short run curves, we can find this by changing the fixed amount of output. Which mean you will have average short run cost curve, or short

run total cost functions. AC

A(c)y 3

AC

2

AC LRAC

1 y

Relationship between short run and long run cost

For low level of y, I’m producing lower level using an old technology. But as y increase I would prefer the newer technology to save cost, this can go on

forever every time my production scale expand.

C’’(Y) C’’’(Y)

C’(Y)

Suppose that 1 firm’s short run cost is represented by C’(Y), then time goes by and the firm realize it has to produce more to fulfil market demand therefore

it needs more machineries to expand production, then another short-term production function will arise, characterized by a greater amount of fixed cost

and you will have a possibly flatter total cost curve C’’(y).

So you see here that at a low level of input it is more efficient to use the first technology, but as soon as the scale become efficiently high, it would be

nd

convenient to produce with the 2 cost curve C’’’(Y)

C’’(Y)

C’’’(Y) C’(Y) LRC(Y)=Lower envelope of short

run total cost

(a curve that tangent all 3 curves)

Here we have 3 short run curves, long run curve will be lower than the other short run curve because in the long run everything is flexible and you can have

all the advantage of the short run curve, therefore will be able to have a lower cost, but the scale of production will remain constant.

There is an optimum amount of output for each of the short run curve (the peak). The long run curve will be below the short run cost curves and tangent all

of them at the optimal output point. This is also true for total cost but not true for marginal cost.

The rule for average cost also apply to total cost so just like in average cost the long-term cost is a lower curve of short term cost, same for the total cost

So just like for average cost, the long term total cost curve will be a lower envelope

The relationship between total cost and unit cost

Suppose you have a total cost curve which is concave then convex, it means that marginal cost increases at first then decrease.

Where do you see your marginal cost here (you will have to look at the tangent of the curve)? Initially the tangents are increasing then they start decreasing

after a certain point

C(Y) Y

What about unit cost?

Well, if you want to know what the average unit cost of this amount Y here, you would take the ray starting from the origin and connecting the origin to this

point here and the slope of that ray is the unit cost, because that is simply the ordinate divided by the axis, so the vertical coordinate divided by the

horizontal one, that’s the link that connect the origin point to any point on the curve. So, you can see that the average cost is at the beginning and the slope

of this ray is decreasing at the beginning and then start increasing

st

If you look at a cost curve which is 1 concave then convex you can say that you have average unit cost which is first decreasing and then increasing, this is a

familiar shape for the average cost curve (the u shape), the kind of average cost curve will correspond to something like this

st

In the short run we say that the average cost curve is given by fixed cost, if you have fixed cost we will have the 1 part of average cost characterized by the

average fixed cost and then average variable cost, eventually average variable cost will increase because average fixed cost are always decreasing but that’s

typical for short run

In the long run, if you want to have the same behaviour, your Average cost curve has to look like this

Concave at the beginning and the convex so eventually you will have decreasing return to scale

MC LRAC

P’

P* Y : minimum efficient scale

X

What is the concept that capture increasing or decreasing return to scale in term of elasticity?

Cost elasticity to output ()

∗

()

That would be the elasticity of total cost in respect to output

In the cost elasticity to output Is greater than 1 that means the cost will decrease by more than 1% when output increase, this is the decreasing returns to

scale, or diseconomies of scale,

If is less than 1 means the cost decrease by less than 1% which signal an increasing return to scale or economies of scale. Economies of scale is linked to unit

cost goes up or down

In the middle of this point we found the minimum efficient scale

In case of perfect competition, unit cost is at the point of minimum so you get 0 profit, you are setting a price equal to min average cost and marginal cost

This is market equilibrium that exist only in the long run of perfect competition, where firms enter and exit market. Until price reach that point, clearly you

will have positive profit.

At p’, the chosen level of output can be found at the cross point between price and marginal cost

Here you can see that price which is marginal revenue is greater than average cost and profit is positive, new firm enter, increase supply therefore price will

be drive down until It reach p*. You are making 0 profit

Plant Size and Flexibility

Suppose the expected demand is 5000 but the demand is risky so there is some liability and you have a probability of distribution so the density around this

expected value

Suppose demand can be represented as follow

F(y) A B Y

5000

Figure 8.8 Probability Distributions of Demand

Distribution L has a low degree of variability from the expected demand level. Distribution

H varies substantially from the expected demand level.

So we have the density and distribution of demand, distribution A and distribution B. Which distribution is riskier?B because the values are more dispersed,

we are less confident that the real values is close to the expected demand

You might also have to choose between plan of different flexibility, how can we represent this degree of flexibility? We can represent them as follow:

LRAC 1

2 Y

4500 5000 5500

Figure 8.9 Alternative Plants for Production of Expected 5,000 Units of Output

Unit costs are lower for plant A than for plant B between 4,500 and 5,500 units of output.

Outside this range, plant B has lower unit costs.

And ì st

You will have to choose between AC1 and AC2. The 1 tech AC1 is more concentrated around the min efficient scale, or more specialized. So corresponding

st

to an output of 5000 unit you have a lower cost than the other, but then once you move off this target, unit cost tends to increase really fast. The 1

technology is specialized for scale production

The second technology is more flexible in the sense that it can also accommodate other technology which are riskier and the unit average cost doesn’t rise

as fast as in AC1. On the other hand, what you have is in the range of 4500-5000, this flexible unit will give you a higher unit cost.

This is a choice under risk and you will have to compare the 2 graphs

If you have dist. A, you have a higher chance to be around 5000 then you possibly should choose the more specialized technology

If you have dist. B, then you will have to choose flexibility

You can cast this into a problem of expecting profit maximization

A problem arise: when you are maximizing profit, are you maximizing also the risk price? No you aren’t, you are only looking at the expected value. You are

completely ignoring this problem regar risk.

So instead of maximizing risk, we have to look at maximizing a concave function of expected profit as if the CEO was risk averse then you would maximize

the utility of the profit and not the profit itself

We are always talking about unit and avg cost, another interesting concept is the concept of learning rate or experience rate

Learning rate

AC AC

t

AC y

t+1

We have two unit cost curves that refer to time t and time t+1. As you move along the curve you get what is known as economies of scale since the AVC

goes down

Clearly worker adapt better on how to use and manage technology but there will always be a way to manage the same technology more efficiently so what

you can expect next year is that the AVC cost curve shift down and you will hve a lower unit cost per same quantity of product

2

1 −

There is a measure of this learning rate

1

So quantity 2 is twice quantity 1. So if for 2 years running, you produce the exact same amount of product then you will get a lower average unit cost if the

learning rate stay the same at 5% so when accumulate output double again (2years later), we expect to have again 5% of reduction. This is important in

term of strategic choice of the firm because maybe you are pretty sure and you expect a decrease in unit cost and try to use price to drive down

competition, you may experience a loss at the beginning but the expect the unit cost to decrease to gain profit

Let’s make an example

Ex ST8.9 = 250000

= 10 + 0.01

(5000) = 522500

(5000) = 10 + 0.01 = 10 + 50 = 60

250000

(5000) = = 50

5000

(5000) = 50 + 60 = 110

522500

′ (5000)

= = 104.5

5000

104.5

1

1− = (1 − ) = 0.05

110

2

Breakeven analysis

This is a kind of analysis that put together cost, price and volume to give you importat information to choose the optimal scale and the degree of operating

leverage: the elasticity of profit to output. How much profit goes up and down in percentage term due to a change in output?

TR

FC TC

VC

AR Q

Q

∗

Q

How do we define profit: total revenue – total cost, we are assuming a fixed price so when you have a new price you have to have a new analysis and we

reason that in term of linear cost function = − = ∗ − ∗ −

∗

= 0 ↔ ( − ) = ↔ =

: =

(

−