ECON 361 - Practice Problems - Elasticity
1. The demand function for a cola-type drink in general is: Qd = 20 - 2P
a. Calculate the point elasticity of demand at prices of $5 and $9.
b. Calculate arc elasticity of demand at the interval between P = $5 and P = $6.
c. At which price would a change in price and quantity result in approximately no change in total revenue? Why?
2. The Teenager company makes and sells skateboards at an average price of $70 each. Over the past year they sold 4,000 of these skateboards. The company believes that the price elasticity of demand for this product is about -2.5. If it decreases the price to $63, what should be the quantity sold? (Hint: use the implied elasticity formula - percentage changes. To determine the percentage change in price - just use $70 as your starting point).
3. If the price of Bob's Bullets increased by 10% and his demand fell off by 15%, what is Bob's implied price elasticity of demand?
4. Suppose that wine sales at Deb's Inn increased 30% in response to her "gentlemen's night" discount of 20%.
a. What is the implied elasticity of demand?
b. Suppose that Deb sells 150 glasses of wine per day. What would be the effect of a 15% increase in wine prices on her sales? (assuming the elasticity you determined in "a" is still correct).
5. If the demand for apples increased by 3% when the price of bananas increased by 6% - what is the implied cross price elasticity of demand?
Are these goods complements or substitutes? Explain.
6. If income increased by 30% and demand for bread increased by 5%, what is the implied income elasticity of demand?
Is bread a normal or inferior good?
Is bread cyclical or non-cyclical?
7. Suppose that the income elasticity of demand is 1.2, and the advertising elasticity of demand is .6. If income falls by 10%, how much would a firm have to increase advertising to make up for the difference?
8. If Betty increased her supply of books by 14% when the price of books increased by 20%, what is Betty's implied price elasticity of supply?
Answers:
1. a. Point elasticity at a price of $5 = -1
Point elasticity at a price of $9 = -9
b. Arc elasticity = 1.15
c. At the price of $5. This is where price elasticity of demand is unitary elastic. This is because this is where Marginal Revenue = zero and total revenue will not change.
2. Since the percentage change in price = 10%, then %change in Qd/%change in P = %change in Qd/10% = -2.5. Solve for % change in Qd = 25%. Therefore, 25% of 4,000 is 1,000 more skateboards sold.
3. Implied elasticity = -1.5
4. a. Implied elasticity = -1.5
b. -1.5 = implies that for every 1% increase in price, Deb will sell 1.5% fewer beers. So a 15% increase will lead to a 22.5% decrease (1.5 x 15), or a decrease of .225(150) = 33.75 glasses of wine per day.
5. Implied cross price elasticity = +.5
They are substitutes. When the price of bananas increased, the demand for bananas would go down. So if the demand for apples is increasing, people must be substituting apples for those bananas they are no longer eating.
6. Implied income elasticity = +.16
Bread is a normal good - when income went up, so did the demand for bread. Bread is non-cyclical. As income changed, the demand for bread did not change very much - so it is not subject to changing incomes as the economy goes to the dogs (or upswings).
7. Remember that for every decrease in income by 1%, demand falls by 1.2%. So since income has decreased by 10%, demand has gone down by 12% (1.2 x 10)
So how much advertising does the firm need to do to increase demand back up by 12%?
For every 1% change in advertising, the firm gets a .6% increase in demand. So to bring that to 12%, the firm would have to increase their advertising by 20% (20 x .6 = 12%) or ? x .6 = 12? Divide 12 by .6 = 20.
8. Implied elasticity of supply = .7 (inelastic)