Managerial Economics

Homework Assignment Three

Due at the beginning of class on Friday, May 17

(66 pts.)

Homework is due at the beginning of class.  SHOW ALL WORK!!

Copy and paste into a word document.  Leave enough space between questions to put your answers. Type your answers!  If you write VERY clearly, you can write out your number answers -- but not your word answers.  But make sure you show all of your work.

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. (2 pts.)

b.  Calculate arc elasticity of demand at the interval between P = $5 and P = $6. (2 pts.)

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).  (2 pts.)

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? (2 pts.)

4.  Suppose that wine sales at Deb's Wine Bar increased 30% in response to her "gentlemen's night" discount of 20%. 

    a.  What is the implied elasticity of demand? (2 pts.)

    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). (3 pts.)

5.  If the demand for apples increased by 3% when the price of bananas increased by 6%,

    a.  what is the implied cross price elasticity of demand? (2 pts.)

    b.  Are these goods complements or substitutes?  Explain. (3 pts.)

6.  If income increased by 30% and demand for bread increased by 5%,

    a.  what is the implied income elasticity of demand? (2 pts.)

    b.  Is bread a normal or inferior good?  Explain.  (2 pts.)

    c.  Is bread cyclical or non-cyclical? Explain.  (2 pts.)

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 (in % terms) would a firm have to increase advertising to make up for the difference? (3 pts.)

8.  The price elasticity of demand for beer has been estimated at -0.84 and of wine at -0.55 (actual numbers from the industry).  Provide an economic explanation (using theory we discussed in class) as to why:

a. both are inelastic. (2 pts.)

b. wine is even more inelastic than beer (2 pts.)

9.  The demand function for a cola-type drink in general is Qd = 20 - 2P. 

a. Calculate point elasticities at prices of $5 and $9. (2 pts.) 

b. Is the demand curve elastic, unitary elastic or inelastic at $5?  At $9?  (2 pts.)

c.  At which price would a change in price and quantity result in approximately no change in total revenue?  Explain your answer. Your explanation should include how marginal revenue relates to elasticity and total revenue.  If you say, "MR = ? at such and such a price", be sure to explain WHY it = ?.  (4 pts.)

10.  The ABC Company manufacturers AM/FM clock radios and sells on average 3,000 units monthly at $25 each to retail stores.  Its closest competitor produces a similar type of radio that sells for $28.

a.  If the demand (with respect to its price) for ABC's product has an elasticity coefficient = -3, how much will it sell per month if the price is lowered to $22? (2 pts.)

b.  The competitor decreases its price to $24.  If cross price-elasticity between the two radios is +0.3, what will ABC's monthly sales be? (2 pts.)

11.  The cross price elasticity of demand for domestic cigarettes with respect to the price of imported cigarettes in Taiwan is +2.78.  Explain what that means.  You should tell me at least two things here and give explanations for each.  (4 pts.)

12.  Suppose a competitor lowers the price of a good by 10% and that the price elasticity of demand = -4, the cross price elasticity = +2, the advertising elasticity  = +3 and income elasticity is = +1. 

a.   Assuming you are holding advertising and income constant, by how much must you lower price in order to keep sales constant? (3 pts.)

b.   Now, assuming your price stays constant (you don't lower it as in "a" above) and also assuming that there is a 20% drop in income,

how much must the firm increase advertising spending in order to keep sales constant?  (3 pts.)

13.  If marginal revenue is above average revenue, average revenue must ________________. (1 pt.)

14.  If marginal revenue is positive, total revenue must be ________________. (1 pt.)

15.  If total revenue is negative, average revenue must be ______________. (1 pt.)

16.  Ceteris paribus, when dealing with an inelastic good, in order to increase total revenue, a firm should _______________ price. (1 pt.)

17.  Now explain your answer that you gave in the question above.  (3 pts.)

18.  You work for a hot springs/spa resort.  Your boss has asked you to come up with a NEW concept using elasticity that might help the spa be more profitable.  He already knows his price elasticity of demand, his cross price elasticity of demand, his income elasticity of demand, his advertising elasticity of demand, his output elasticity of demand with respect to inputs and his price elasticity of supply for all of his products.  So he doesn't want any of those from you.  Come up with something new for your boss:

Your Concept? (2 pts.)

Your formula? (2 pts.)

It's use to help the sap (your boss), oh I mean the spa be more profitable? (2 pts.)