# Marginal revenue and the relationship with elasticity of demand

Topic #35
Eric Nault
Shane Tullis

Marginal Revenue

Marginal revenue is the measurement of the change in total revenue (TR) divided by the change in quantity sold (Q). Another way of looking at marginal revenue is to think about a production process. Marginal revenue is the total revenue generated before and after a one-unit increase in the rate of production. As you can see from the Graph 1, demand and marginal revenue, in order to increase production, suppliers need to lower there prices and this will lower their marginal revenue and increase their marginal costs. Suppliers will continue to produce increase quantities until their marginal costs equal their marginal revenues. At this point, suppliers are in profit maximizing condition. A good example of this term in the "real world" is the price of chewing gum. For this example the current price of chewing gum is \$1 and the demand is 10 units at this price. If the marginal revenue and demand curves are linear, in order for this supplier to increase output it will need to stimulate consumers with a lowered price (P<\$1).

More about Marginal Revenue (discussed as Marginal Value) is located in this MBAecon site as well.

Elasticity of Demand
This is a value that is calculated by the percentage change of demand for a product divided by the percentage change in the price of a product. Elasticity of demand is a valuable calculation to predict how suppliers or consumer will respond to a change is price of a demanded product. If we use the chewing gum example and say that this suppliers choses to lower it's cost by \$.25 for a new price of \$.75 and the demand is now 12 units. With these values we can calculate this consumer own price elasticity of demand by dividing the percentage change in quantity (12-10)/10=.2 by the percentage change in price (1-.75)/1=.25. For this example the own price elasticity of demand is .8 which shows that the demand for chewing gum, in this example, is rather inelastic to price changes.

Formula for Own Price Elasticity of Demand

Ex = Own Price Elasticity of Demand of Good x at Qx and Px below
%<| Qx = the Percentage Change in Quantity Demanded of Good x
%<| Px = the Percentage Change in Price of Good x

E = ( %<| Qx) / ( %<| Px )

More about Elacticity of Demand is located in this MBAecon site as well.

Relationship Between Marginal Revenue and Elasticity of Demand
The relationship between MR and ED is that each measurement is important in managerial decisions on price and quantity. For example if a managers understands the elasticity of demand for its product, he or she will be able to make in informed decision on how consumers will react to a price increase or decrease. If the manager decides to raise the price of the product and demand for the product is elastic, consumers will likely purchase less of the product.

Formula

MR = Marginal Revenue
P = Price of the Good
E = Own Price Elasticity of Demand

MR = P * [ ( 1 + E ) / ( E ) ]

Formula Consequences

• When E is between negative infinity (exclusive) and -1 (exclusive), then demand is elastic, and the formula implies that MR is positive.
• When E = -1, demand is unitary elastic, and the formula imlies that MR is positive.
• When E is between -1 (exclusive) and 0 (exclusive), demand is inelastic, and marginal revenue is negative.

Graphs

Graph 1 Graph 2

Additional Principles

A.) Total Revenue Test - if the demand is elastic, then an increase in price will lead to a decrease in total revenue. This is true because, according to the formula, the decrease in quantity sold, as a percentage, will more than counteract the increase in revenue from charging larger pirces. So on the contrary, if demand is elastic, then a decrease in prices will lead to a increase in total revenue.

On the other hand, if the demand is inelastic, then an increase in price will lead to an increase in total reveune. This is true because, according to the formula, the increase in revenue, as a percentage, is larger than the decrease in demand that will result from the pirce increase. So on the contrary, if demand is inelastic, then a decrease in price will lead to an decrease in total revenue.

B.) Total revneue is maximized at the point where demand is unitary elastic (where the own price elasticity of demand is equal to negative one.

Real World Examples
Example 1: Jesse works at the Superplex 8, which is a major movie theatre in his town. His manager, Sharon, has recently hired economic consultants that have told her that at the current of popcorn, the elasticity of demand is -0.75. Sharon tells Jesse to raise the price of an order of popcorn from \$5 to \$6. Jesse, a mathematics student, says, "That is a 20% rise in the price of popcorn!" Customers will revolt and buy many fewer orders of popcorn, or none at all."

Answer 1: While Jesse is mathematically correct, he could use a little help in economics. Since the elasticity of demand for popcorn is -0.75, that means that the demand is inelastic at that point. Taking it further, this means that the total revnue will rise with an increase in the price.

External Links and references:
1) Managerial Economics and Business Strategy (5th Edition), pages 74-76 and 83-84 – Michael R. Baye
2) www.wikipedia.com - topics "Marginal Revenue" and "Price Elasticity of Demand"
3) Revenue and Demand from ingrimayne.com.
4) Marginal Revenue and Demand elasticity from Amosweb.com.
5) Marginal Revenue for a Monopolist from University of Toronto.
6) Great presentation on topic from University of California at Santa Barbara.
7) Economics interactive tutorial about monopoly price and output from University of South Carolina.

Example Multiple Choice Questions:
1) Each week Bill buys exactly 7 bottles of cola regardless of its price. Bill's own price elasticity of demand for cola in absolute value is:
a. 0
b. 3
c. 1
d. .1

2) Suppose the own-price elasticity of demand for good X is -0.5, and that the price of good X increases by 10%. What would you expect to happen to the total expenditures on good X?
a. no change
b. increase
c. decrease
d. not enough information

3) The own-price elasticity of demand for apples is -1.2. If the price of apples falls by 5%, what will happen to the quantity of apples demanded?
a. 1%
b. 4%
c. 5%
d. 6%

4) Which of the following is a correct representation of the profit maximization condition for a monopoly?
a. TR=ATC
b. MC=MR
c. MC=P
d. MC>MR

Answers
1) a
This is an example of a perfeclty inelastic demand. Regardless of changes in price, Bill will always purchase 7 bottles of cola. The demand curve is perfectly vertical from Q=7 on the x-axis
2) b
The equation for Ed=(%change in Q)/(%change in P). As P increases by 10%, the % change in Q is Ed(%change in P) -0.5(.10)=(-.05). In this problem the quantity, or total expenditures, are decreased.
3) d
The equation for Ed=(%changein Q)/(%change in P). Q=(-1.2)*(-.05)=0.06 or 6%
4) b