# Econ 136: Working with Economic Data

## Class 6 -- Elasticity and Marginal Revenue

So far we've demand data to illustrate changes in consumer and social welfare.   Now, I want to shift to the role of demand in individual firm behavior in imperfectly competitive markets.  (The position of the demand curve is irrelevant to the decision making of firms in competitive industries.)

Example:  Suppose you are the marketing manager for a branded toothpaste.  The chief financial officer of the company would like to increase profits -- or at least stay ahead of rising costs.  She'd like your opinion about the impact of a 10 cent increase in the price.

The textbook response is not helpful without quantitative data.  (What is that textbook response?)

How do we go about obtaining the necessary data.

In practice, we can't observe demand curves or full demand schedules.  We know where we are (the quantity demanded at existing prices) and we have some sense of the shape of the demand curve near the market outcome -- i.e., we have a sense of the responsiveness of demand.

Economists measure the responsiveness of demand, the shape of the demand curve with the price elasticity of demand:

e = -(%D in quantity)/(%D in price)

• demand is inelastic if 0 £ e < 1 -- quantity is relatively unresponsive
• demand is elastic if e > 1 -- quantity is relatively responsive
• demand has unitary elasticity if e =1

Empirical research suggests that demand elasticities are fairly stable for most commodities and highly differentiated products and that the elasticity does not change much when demand shifts out or back.

Current price = \$2.39/tube

Current Sales = 12.6 million tubes

Estimated demand elasticity = 1.3

We can use these data to project changes in sales, hence changes in revenue.  So, as marketing manager you should be able to give the CFO a fairly estimate of marginal revenue.  By comparing this with marginal cost (which may well change as a result of the change in quantity sold), the CFO can determine whether the 10 cent price hike will increase profits.  Generating the costs data is the task of the production and accounting departments -- you need to put together the revenue data.

Theory tells us that there is a precise relationship between marginal revenue and the elasticity of demand.

R = PQ

From calculus, for infinitessimal changes:

dR = PdQ + QdP -- this is the total differential of R

Dividing through by R = PQ, we get

dR/R = PdQ/PQ + QdP/PQ or

dR/R = dQ/Q + dP/P

In words, the percentage change in revenue equals the sum of the percentage changes in quantity and price.

Theory yields two major insights

• The changes in P and Q are constrained by the demand relationship
• The relationship is summarized by the elasticity of demand

With inelastic demand

%D in quantity < %D in price implies %D in revenue from an increase in quanity (because of of a price cut) will be negative;  hence MR (=dR/dQ) < 0

With elastic demand?

So our toothpaste example, implies that raising price will actually decrease revenue.   But, this isn't the end of the story, because it also will reduce costs.  If the firm had been operating where MR < MC then raising price (reducing output) is the smart strategy since it will raise profits.  Hence, we need an estimate of the actual change in revenues resulting from the price hike.

For this purpose, elasticity raises a problem -- since it's definition is ambiguous for non-infinitessimal changes.

Example:  Suppose a price rise from \$1.00 to \$1.20 results in a drop in sales from 10,000 to 8,000 units.

What's the percentage change in price?  in quantity?

What's the elasticity of demand?

Suppose we lower price from \$1.20 to \$1.00.

What's the percentage change in price?

What's the percentage change in quantity?

So now the elasticity of demand is 1.5.

The calculated elasticty is sensitive to the choice of P and Q on which to base the percentage changes.  The usual solution is to choose the midpoint between the before and after price/quantity for the denominators of the percentage changes.  This leads to the arc elasticity.

But, as marketing manager you don't know one of those end points.

There are a couple of solutions -- the easiest to implement is to use the original P/Q combination as the denominator for the percentage changes and make the percentage changes symmetric around the original point.  The procedure is easier to demonstrate than to describe.

Treat the 20 cent price change as half of price change symmetric around \$1.40.

1) Doubling DP and dividing by P yields the percentage change in price.

2) To obtain the forecasted percentage change in quantity, we can manipulate the elasticity definition.

e = -(%D in quantity)/(%D in price) to get

%D in quantity = -e*(%D in price)

3) Obtain the symmetric change in quantity from the percentage change

%D in quantity = (D in quantity)/Q

D in quantity = (%D in quantity)*Q

4) The actual change is half the symmetric change

5) Add the actual change to the original quantity to obtain the projected quantity.

So a 10 cent price increase will reduce toothpaste sales rom 12.6 million tubes to just over 11.2 million tubes.

What will be the effect on revenue?

What's current revenue?

What's projected revenue?

Incremental revenue is projected minus current.

Marginal revenue is incremental divided by the change in quantity resulting from the price hike.

What should the CFO do?

Suppose estimated MC = .70?

.50?

For Monday:  Read the section of your Principles textbook on National Income Accounts or take a look at this discussion on the Web:   Follow the top four links under Reading Sections.