Chapter 3: Problems 3, 4, and 7
3. The Olde Yogurt Factory has reduced the price of its popular Mmmm Sundae from $2.25 to
$1.75. As a result, the firm’s daily sales of these sundaes have increased from 1,500/day to
1,800/day. Compute the arc price elasticity of demand over this price and consumption quantity
range.
ED = [(1800 1500)/(1800+1500)]/[(1.75  2.25)/(1.75 + 2.25)], so ED = 0.727 for Mmmm Sundaes.
This is inelastic in this price range. It suggests the Olde Yoguart Factory should consider a price increase,
as this will increase revenues and reduce costs.
4. The subway fare in your town has just been increased from a current level of 50 cents to $1.00
per ride. As a result, the transit authority notes a decline in rider-ship of 30 percent.
a. Compute the price elasticity of demand for subway rides.
b. If the transit authority reduces the fare back to 50 cents, what impact would you expect on the
ridership? Why?
a.
ED = 30%/+100% = 0.3 is the price elasticity for subway rides. This is inelastic.
b. Ridership probably would not return to the original level because some people may
have invested in alternatives (cars, etc.) or found other transit options that they are
reluctant to give up.
7. In an attempt to increase revenues and profits, a firm is considering a 4 percent increase in
price and an 11 percent increase in advertising. If the price elasticity of demand is −1.5 and the
advertising elasticity of demand is +0.6, would you expect an increase or decrease in total
revenues?
Any demand function can be decomposed into percentage changes and elasticities of the component parts.
If Q = f(P, A), where P is price, A is advertising, ED and EA are price and advertising elasticities, then:
%Q = %P(ED) + %A(EA) = (+4%)(-1.5) + (+11%)(.6) = +.6%. We expect a small increase in
quantity of .6%. Total revenue will increase since both price and quantity increase. With 6% higher
prices and .6% higher quantity, revenue rises about 6.6%. The prediction is less precise than this analysis
suggests, because it is based on calculus which works best for very small changes.
Chapter 4: Problems 5, 6, and 7
5. General Cereals is using a regression model to estimate the demand for Tweetie Sweeties, a
whistle-shaped, sugar-coated breakfast cereal for children. The following (multiplicative
exponential) demand function is being used:
Demand for Tweetie Sweeties by General Cereals question:
a.
The price elasticity is -2.15, which is elastic.
b.
The advertising elasticity 1.05.
c.
The population elasticity is 3.70. A one-percent increase in the population over under the
age of 12 will lead to a 3.7% increase in the demand for Tweetie Sweeties.
6. The demand for haddock has been estimated as log + b log P + c log I + d log Pm
where of haddock sold in New England per pound of haddock
measure of personal income in the New England region
index of the price of meat and poultry
a. Determine the price elasticity of demand.
b. Determine the income elasticity of demand.
c. Determine the cross price elasticity of demand.
d. How would you characterize the demand for haddock? Apparently the Haddock is plentiful
since it a white fish. New England has lots of ocean access to fish.
e. Suppose disposable income is expected to increase by 5 percent next year.
Demand for haddock question:
a. The price elasticity is -2.174, which is elastic.
a.
b.
c.
The income elasticity is 0.461, which is a normal good, but a necessity like most food items.
The cross price elasticity with meat and poultry is 1.909. Fish and meat/poultry are
substitutes.
Haddock is elastic, a necessity, and other meats are close substitutes.
d.
A 5% increase in income leads to a (.461)(5%) = 2.305% increase in the demand for
Haddock.
7. An estimate of the demand function for household furniture produced the following results:
1.08 .16 -.48
Y R P
where expenditures per household
personal income per household
of private residential construction per household
of the furniture price index to the consumer price index
a. Determine the point price and income elasticities for household furniture.
b. What interpretation would you give to the exponent for R? Why do you suppose R was included
in the equation as a variable?
c. If you were a supplier to the furniture manufacturer, would you have preferred to see the
analysis performed in physical sales units rather than dollars of revenue? How would this change
alter the interpretation of the price coefficient, presently estimated as −0.48?
Demand for furniture question:
a. The income elasticity of furniture is 1.08, which puts it in the luxury category. The price
elasticity (using real prices) is -0.48, which is inelastic.
b. R is the value of private construction per household. For a 1% increase in the private
residential construction, there is a .16% increase in furniture purchases. The greater the
amount spent by families on their housing, the more furniture that they acquire.
c. If all furniture was alike, using physical units could work. Some furniture is elaborate, with
rare wood or costly fabrics, while others are cheaply constructed. Revenue is not perfect,
but it allows chairs, tables, and Armoires to be added together in dollar values. In units,
the price elasticity is shows how a 1% price jump in real prices affects units sold; whereas in
revenue, the price elasticity shows how a 1% real price increase impacts the dollar value of
goods sold.