Chapter 3/Demand Analysis

Chapter 3/Demand Analysis

Chapter 3

Demand Analysis

______

Solutions to Exercises

1. a. Ecross = [(4,500  6,000)/(4,500 + 6,000)]/[(450  600)/(450 + 600)]

So Ecross= 1.00

b. Yes, they are. A 1% decrease in price by Spring City Stove Works’ microwaves leads to a 1% decrease in sales by Potomac. Other factors that could influence the observed relationship are: (a) seasonality in the demand for new ovens, (b) unfavorable publicity by government agencies about radiation or other dangers associated with ultrasonic ovens, and (c) an economic recession or boom during the period of the observation.

c. −3.0 = [(6,000 − 4,500)/(6,000 + 4,500)]/[(P2− 500)/(P2 + 500)]

So P2 = $454.54

2. ED = %Q/−20% = −2.2, or %Q = +44% in personal computers sold.

3. ED = [(1,800 1,500)/(1,800+1,500)]/[(1.75 − 2.25)/(1.75 + 2.25)]

So ED = −0.727 for Mmmm Sundaes.The arc price elasticity of Mmmmm sundaes is in the inelastic range of demand. It suggests that the Olde Yogurt Factory should consider a price increase, as this will lead to an increase in revenue and a decrease in cost.

4. a.ED = −30%/(+0.50/0.75)% =−0.45 is the price elasticity of demand for subway rides. The price elasticity of demand for subway rides is in the inelastic range of demand.

b. Ridership probably would not return to the original levelbecause some people may have invested in alternatives (cars, etc.)or found other transit options that they would bereluctant to give up.

5. Since MR = P( 1 + 1/ED ), we can find P after substituting for both MR and the price elasticity: 15 = P( 1 + 1/(−1.2) ). This implies that 15 = P(0.167) or P = $90.

6. a.Bicycle demand in Holland is Q = 2,000 + 15Y − 5.5P

P = 150 guilders; Y = 15(000) guilders
Solving for Q: Q = 2,000 + 15(15) − 5.5(150) = 1,400

ED = −5.5(150/1400) = −0.59

The price elasticity of demand for bicycles is in the inelastic range of demand.

b.Ey = 15(15/1400) = 0.16. Since the income elasticity of demand for bicycles is positive, bicycles are income-superior goods.

7. Given the change in price and the change in advertising, the combined effect on the quantity demanded would be: %Q = %P(ED) + %A(EA) = (+4%)(−1.5) + (+11%)(0.6) = +0.6%

We expect a small increase in quantity demandedby0.6%.Total revenue will increase since both the price and the quantity demanded increase. With 4%increase in price and 0.6% increase in quantity demanded, revenue rises by about 2.4%.

8.For the Stopdecay Company, we find:

a. Ecross = [(6,500 8,000)/(8,000 + 6,500)]/[(30  35)/(30 + 35)], which is −0.1,034/−0.077, so Ecross = +1.34. The cross elasticity between Stopdecay’s toothtbrush and Decayfighter’s toothbrush is positive.Therefore, the electric toothbrushes are substitutes. A 1 percent increase (decrease) in the price of one toothbrush results in a 1.34 percent increase (decrease) in the quantity demanded for the other.

b. The price cut by Decayfighter leads to a 10.34% drop in quantity of brushes sold by Stopdecay. Solving for the price,Stopdecay would have to charge in order to sell the same number of units as before:

−1.5 = %Q/ %P = +0.1034 / %P, or %P = −0.0699. Therefore, Stopdecay would have to reduce the price of its electric brush by7%.

c.After Decayfighter cuts the price of its electric toothbrush, the quantity supplied by Stopedecaydrops from 8,000 to 7,173 (10.34% drop).The average monthly total revenuewill be 7,173 × $25= $179,325. In response to Decayfigher’s price cut, if Stopdecay drops the price of its electric toothbrush by 7%, the quantity supplied by it would return to 8,000 at a price $23.25. The average monthly total revenue will be $186,000.

d.Stopdecay should lower the price of its product only if the additional revenue earned from the price cutis greater than the additional costs incurred because of the price cut. The decrease in price produces an extra revenue of $6,675. If the cost of each toothbrush is greater than $8.07, then the additional costs incurred because of the price cut will be greater than theadditional revenue.

9.Sydney Transportation data permits us to predict sales based on price and cross-price elasticities. If the only change from 2005 to 2006 is the increase in parking rates, then the cross price elasticity between bus ridership and downtown parking rate would be+0.2. This can be calculated by using thearc formula or by usingthe base rateapproach.By using the arc formula:

%QRiders/%PParking =0.2 =[(Q20065,000)/(Q2006+5,000)]/[(2.50  1.50)/(2.50+1.50)]

Q2006 = 5,526

Other economists tend to make the problem a bit easier by using the base level:

[(Q2006 –5,000)/5,000]/[(2.50 −1.50)/1.50] =0.2

The higher parking prices lead to prediction of increased ridershipin 2006, where Q2006 = 5,667.

If the only additional change in 2007 is an increase in bus fares, then we can use own price elasticity at the higher price level. Price elasticities tend to increase (in absolute value) as prices rise.

Byusing the arc formula:

%QRiders/%PFares= 1.2 = [(Q20075,526)/(Q2007+5,526)]/[(1.25  1.00)/(1.25+1.00)]

Q2007 = 4,238

Using thesimplerbase rate approach: [(Q2007 –5,667)/5,667]/[(1.25 − 1.00)/1.00] = −1.2

The 25% fare hike leads to a prediction of decreased ridership in 2007, whereQ2007 = 3,967.

10.Reliable Aircraft Company provides data suitable for arcprice and arc income elasticity estimation.However, caution should be used in interpreting these results as some other factors other than disposable income may also have changed.

1. ED2007 = [(450 −525)/(450+525)/2]/[(8,000 −7,200)/(8,000+7,200)/2] = −146

The arc price elasticity of demandlies in the inelastic range of demand.

1. Since income did not change from 2006 to 2007, it is not possible to estimate the income elasticity.However, it is possible to estimate the arc income elasticity of demand between 2007 and 2008. EY2008 = [(400 − 450)/(400+450)/2]/[(590 −610)/ (590+610)/2] = +3.53. The arc income elasticity of demand is greater than one. Therefore,airlines are luxury goods.

1. If income rises by $40 billion in 2007, then by using the arc formula, the prediction of sales in 2009can be calculated as follows:

EY = 3.53 = [(Q2 400)/(Q2+400)]/[(630  590)/(630+590)]

Q2= 505 airplanes

1. Since Q =f(P,Y), where P is price and Y is income,

%Q = %P(ED) + %Y(EY)

= [(8,500 − 8,000)/(8,000+8,500)/2](−1.46) + [(630 −590)/(630+590)]( 3.53) = +14.3%

Using the average quantity, [(Q2 + Q1)/2], as the base to compute the percentage change:

%Q = 14.3% = [(Q2 400)/(Q2 + 400)/2](100)

Q2 = 461.6 airplanes

11. It is likely that the taxes are unrelated to urban congestion as, clearly, congestion is worse in L.A. than in Toronto. Rather, it is more likely that gasoline taxes are a means to levy general taxes without the public objecting too much. However, economic knowledge of price elasticities may suggest that in more rural households as in Canada, demand for gasoline maybe less price sensitive than in the U.S. where urbanites are offered more mass transit alternatives. Furthermore, Canada is less populated than the US and also has an intercontinental highway system. Canada uses some toll roads, but much of the system is constructed using gasoline taxes. If Canada builds 50% more roads per person, then this could explain the 50% higher gas tax.

12.We can view the price reduction in a car as being offset by switching costs. If there is a high switching cost (supposethe switching cost for the old couple is $4,000), a fixed coupon of $5,000 off a car is only worth $1,000 off. If the German couple has a switching cost of $500, then the same $5,000 coupon is worth $4,500 off (much more). It maybe that the German couple has a greater price elasticity than the (retired) old couple. Indeed, for the old couple, it is as if there is an unseen full cost of a car (with a switching cost) that is not the same as the sticker price.

13.The newly married couple views a Taurus as an aspirational purchase compared to a Ford Focus.

The German couple already owns a used Taurus. They view the new one as a replacement. As with most durable goods, the price elasticity is high in this case,because a decision to replace a product can be delayed. The timing of such purchases is impacted by temporary incentives, such as the coupon. They arethe most likely to respond to the $4,000 coupon.

The retired couple with a Crown Vicviewsa Taurus as a step backward (in size and in status). They are the second least likely to be swayed by the coupon offer.
The young French immigrant couple already aspires to purchase a Volvo. The couple views a Taurus as an inferior purchase. They are the least likely to be swayed by the coupon offer.

Solution to Case Exercise: Polo Golf Shirt Pricing

The table can be completed by using marginal revenue to complete the total revenue column for quantity of 10 or higher. The area with a square around it is the completed table.

Quantity / Price / Total Rev / Marginal Rev / Marginal Cost
0 / $50 / $0 / $0 / $28
1 / $48 / $48 / $48 / $28
2 / $46 / $92 / $44 / $28
3 / $45 / $135 / $43 / $28
4 / $44 / $176 / $41 / $28
5 / $42 / $210 / $34 / $28
6 / $40 / $240 / $30 / $28
7 / $38.31 / $268 / $28 / $28
8 / $36.50 / $292 / $24 / $28
9 / $34.50 / $311 / $19 / $28
10 / $32.65 / $327 / $16 / $28
11 / $30.86 / $340 / $13 / $28
12 / $29.13 / $350 / $10 / $28
13 / $27.42 / $357 / $7 / $28
14 / $25.75 / $361 / $4 / $28
15 / $24.03 / $361 / $0 / $28
16 / $22.47 / $360 / -$1 / $28
17 / $20.91 / $356 / -$4 / $28
18 / $19.36 / $349 / -$7 / $28

1. Marginal revenue for the fourth shirt is $41 even though its price is $44. To sell more shirts, the Ralph Lauren outlet store needed to reduce the price by $1.
2. The marginal revenue of the fourth shirt is $41 and the variable cost is $28. Therefore, there is an operating profit of $13 on the fourth shirt.
3. Selling the seventh shirt per day at a price of $38.31 required the price to be reduced from $40 to $38.31.The total revenue increased from $240 to $268. Hence, there was an increase of $28 in total revenue. The decision to sell the seventh shirt is a “break point” because at this quantity, the marginal cost of selling each additional shirt is equal to the marginal revenue earned from selling that additional shirt.
4. Revenue lost per unit sale relative to the price that would sell six shirts per color per day = $268/7 − $240/6 = −$1.714.
5. The answers are markedin the table above.
6. Sales personnel working on commission (a given percentage of sales revenue) would prefer the $24.07 price that would give a total revenue of $361, selling 15 shirts a day.
7. This is not a profit maximizing decision. If the store sells beyond the 7thshirt, then the marginal revenue from selling any additional shirt would beless than thetotal variable costs incurred, and profits would decrease with each additional shirt sold. “Selling at a negative margin” implies selling at a net loss.
8. The marginal operating losson the 14th shirt is $24. Onthe 12th shirt, the marginal operating lossis $18. Onthe 10th shirt, the marginal operating loss is $12. Operating loss arises when marginal revenue is less than the total variable cost
9. The optimal shirts sold is where MR = MC, which holds at 7 shirts sold at $38.31 per shirt. The optimal markup is 36.82% [$38.31/$28 = 1.3682 or 36.82%]. The dollar markup is $10.31.

1

© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.