Pricing of Multiple Products

Normally the standard theory states that a firm prices where MR = MC (as you know).

But sometimes it is very difficult to determine what MR and MC are.

It becomes more complicated for a manager to set price when his firm has interrelated products.

Example:  Proctor and Gamble sells both Luvs and Pampers – which are substitutes for each other.  A change in one price will affect the demand for the other. 

Plus, if both products use the same production facilities – the firm must determine how costs are to be allocated between the two goods.

When firms produce interrelated products – must consider four types of interrelationships:

1.       Products with interdependent demands

2.       Joint products (complements in production)

3.       Products with common costs

4.       Intermediate products (transfer pricing)

Let’s take them one at a time.

1.        Products with interdependent demands

These are either substitutes or complements.

The basic objective of the firm should be to determine the prices that gives them the best total profit for the firm, rather than profit earned by individual products.

Consider the MR equations for both products (assume the firm produces two products – X and Y).

MRx =   Change in TRx/Change in Qx + Change in TRy/Change in Qx.

MRy =   Change in TRy/Change in Qy + Change in TRx/Change in Qy.

The signs of the interdependency terms depend on the nature of the relationship:

Complements – both terms (+)

Substitutes – second term will be (-)

If we want to go to the point where MR = MC, then the output of X should increase (if they are complements) until:

Change in TRx/change in Qx + Change in TRy/Change in Qx = MCx

So we will produce less than we otherwise would have if we ignored the extra revenue generated through the sale of Y OR

On the other hand, if they are substitutes, then we will probably overproduce if we ignore the affect on Y.

In addition to taking interdependendencies into account – must also consider the reactions of competition.

Example:  Texas Instruments introduced home computers and options like disk drives and printers.  They knew no one would buy the options without the basic machine – so they sold the basic computer for a lower price than otherwise but this stimulated sales on options – which they priced much higher than otherwise.  This worked for a while – until the competition started offering the options at lower prices.  They had to change their pricing strategy.

2.        Joint Products (Complements in Production)

Products that are related in production – in this case goods are jointly produced in fixed proportions.

Example:  Beef and hides.

 Must consider the two as a package = the sum of the MR of the two goods. 

Problem Example:

Assume the MC of producing the joint products is:  MC = 30 + 5Q

Where 30 = per unit fixed cost and 5 = per unit variable cost.

Demand and MR equations are:

Beef - Qd = 60 – 1P, so P = 60 - 1Q and MR = 60 – 2Q

Hides – Qd = 40 - .5P, so P = 80 – 2Q and MR = 80 – 4Q

If we add the two MR curves:  MR = 140 – 6Q

If we equate MR = MC:

140 – 6Q = 30 + 5Q

110 – 6Q = 5Q

110 = 11Q

Q = 10

So if we substitute 10 into the Price equations:

P (beef) = 60 – 1(10)

P = $50

And

P (hides) = 80 – 2(10)

P = $60

However, before concluding that these prices are the best we can do – need to make sure they wouldn’t lead to a negative MR for an individual product – that we have actually gotten to the point where the next unit produced brings TR down.

MR (beef) = 60 -2Q

MR = 60 – 2(10)

MR = 60 – 20

MR = 40

AND

MR = (hides) 80 -4(Q)

MR = 80 – 4(10)

MR = 80 – 40

MR = 40

Because both MR’s are positive, these prices will give us the most profit possible (given our information).  If MR for either product is negative, the quantity sold of that product should be reduced – and maybe not even sold at all.  Be careful that the package deal doesn’t overstep the individual boundaries. 

This could happen when the joint MC is very low.  A firm should never produce an output rate where MR is negative.

Graphically:

Of course:  As Koch points out – we need to actually use our opportunity costs as real costs for our decisions.  So, for example, if the cost of disposing of, say the hides, is very high, then we need to add that opportunity cost (of not selling them) to the cost of only selling hides – that will change the story.

3.        Products with Common Costs

Common costs are costs that cannot be assigned to any specific product or service.

Example:  High voltage transmission lines – serves residential customers electricity but also industrial and commercial.  How should the costs be assigned?  (Basically, the service will be provided even if one group is not served – costs are still there).

a)    Fully distributed cost pricing –

This allocates a portion of the firm’s common costs to each product or service.  All common costs are distributed among the products and services for the firm.

Then set the price of each such that it covers the designated portion of common costs plus costs that are directly related to the provision of the product or service.

This assignment must be arbitrary – but – the choice of allocation scheme may have an impact on the price set and hence the quantity demanded of the goods and services provided by the firm.

Example:  Firm has two services – secretarial work and data processing.

$10 million – common costs, must be paid even if neither service is provided.

Provision of the first service is very labor intensive – 80% of all labor costs involve the secretarial workers.

In contrast, data processing is capital intensive, 80% of all capital costs involve this service.

Fully distributed costs chosen – two possible schemes?

1.        Apportion common costs on the basis of labor costs resulting from each service.

2.       Apportion common costs on the basis of capital investment resulting from each service.

How would each affect the price set for each service?   

If 80% or 8 million is assigned to secretarial work, the price would have to be relatively higher vs. 20% or 2 million for data processing and vice versa.

Although a firm must cover its common costs – it is not necessary that the price of each product be high enough to cover an arbitrary apportioned share of common costs. 

Price must cover incremental or MC – as we have learned before.  As long as it exceeds MC, there is an increase in total profit by supplying the product.  Hence decisions, as always, should be based on an evaluation of MC or incremental costs.

Example:  Suppose there is a train that runs from San Francisco to San Diego.  The train owners are wondering if they should stop in Los Angeles?

The added cost would be energy due to extra passengers and the station.

The common costs are the rails, trains, engines, cars, etc. = $120 per train trip (one way).

It is determined that a bus ticket to LA is the main competition and if the train is to compete – the price should not go above $30.

Should they offer the service to LA?

If we share all common costs – the fare would have to be $40 ($120/3)

Using MC – with rail lines in place and already operating the additional expense of transporting a passenger from SF to LA is $15.00 (assuming capacity is not an issue and there isn’t an opportunity cost of losing a passager going form SF to SD).

The service should be offered and priced between $15 and $30 – the train can cover its MC plus contribute toward the common costs!

Total profit of the firm would increase.  AND in fact the price from SF to SD could be reduced (their common costs have gone down due to the LA contribution).

Obviously common costs have to be paid somewhere – not all products in a firm can be priced by their incremental costs.

But it is not necessary that all products carry some of this cost.  As long as price exceeds incremental costs – total profit can be increased by providing the product.

So the use of the fully distributed costs can lead to poor pricing decisions.

4.       Intermediate Products (Transfer Pricing):

Vertically integrated firm – more than one stage in the production process.  So a firm has or produces intermediate goods – needed as inputs at a later stage of the firm’s operations.

Profit Centers (via Koch) – are a way of dealing with:

a.        How to measure the productivity of each product

b.      Diseconomies of scale

Once a firm has vertically integrated, can break it up into separate units of operations  or divisions with their own function and management.  Each management team is rewarded on the basis of the unit’s profit or performance.

As Koch discussed, the problem arises of how to determine the profit or value creation of each unit.

If one unit is to provide an input for the next stage of the production process – revenue will depend on the price that is charged for the intermediate good.  A high price will increase profit at earlier stages and vice versa.

Also – an incorrect price set for an intermediate good can affect the total profit earned by the firm.  Especially if each unit tries to maximize profit – total profit for the firm could go down.

Example:  Let’s assume two stages of production:  1.  Rolls of paper manufactured and 2.  Paper cut into tablets and sold.

Two Cases:

a.        External Market – there is an external market for the rolls of paper – can sell and also stage 2 can buy elsewhere.

Here – there is no price decision to be made.  Charge the market price.

That tells the firm the actual market value of the paper.

Even if there is excess supply within the firm – can sell it in the external market.  Or if not enough, can buy from the external market.

b.       No external market.  The intermediary is specific to the firm.  In this case, the theory goes – to determine the price that would maximize profit for the overall firm –

Graph:

From the firm’s perspective, the MC of the product is the sum of the MC of tablets and of paper.  So the best strategy is to set MC (total) = MR and then determine price at that point.

Both divisions supply enough to meet Qmax.

The paper unit should be required to set its price = Mcpaper – this way the paper division will supply just enough paper to produce Qmax units of tablets.

This again, is trying to use consumer demand (value) to determine the price as best as possible.

Cost Plus Pricing

Another pricing strategy that a firm could use is cost plus.  Instead of trying to maximize profit, many managers say they set prices to achieve a target rate of return on investment.

Cost Plus pricing is the most widely used procedure for achieving the targeting rate of return.

Setting prices that cover the cost of purchasing or producing a product plus enough profit to allow the firm to earn its target rate of return.

(This is probably because firms don’t know what the maximum profit rate is !!!)

Two steps:

1.        Determine the cost of acquiring or producing the good or service.  ATC = AVC + AFC, which are determined from TVC/Q and TFC/Q.

The problem with the computations is – the quantity is used to calculate the price – but quantity is determined by price!!

So an assumed quantity is used.  Usually some % of the firm’s capacity.

2.        Determine the mark-up over costs.  If the targeted rate of return requires $X of total profit – the mark-up over costs on each unit of output will be X/Q or average (per unit) profit.

Hence the price will be:  P = AVC + AFC + X/Q

Advantages:

a.       Easy to calculate.

b.      Provides a clear justification for price changes.

Shortcomings:

a.       Doesn’t take demand into account (BIG SHORTCOMING)!

b.      Costs could be wrong – based on historical data.

c.       Usually based on fully-distributed costs and its problems.

This method is often used by regulated, government – granted monopolies (like the post office) – can you explain why?

What incentives does this create?