The cross price elasticity coefficient between Blackhawks tickets and Chicago Bulls tickets is 4. The income elasticity coefficient for Chicago Bulls tickets is 5. The cross price elasticity coefficient between Chicago Bulls tickets and parking at the United Center is – 8 b. The Bjorn Borg Tennis Mfg. Company estimates that its demand function for tennis rackets is as follows: Qº = 200 – 2P +31 +.5A where Q is quantity demanded per month, P is the product’s price (in dollars). I is per capita disposable income in thousands of dollars), and A is the firm’s advertising expenditures (in thousands of dollars per month). Is this good a normal or inferior good? Explain. During the next decade, per capita disposable income is expected to fall by about $3000. What effect will this have on the firm’s sales? Ignore parts a, and b. Suppose P = $75, I = 10 units (i.e, $10,000), and A = 6 units (ie. $6,000 find Q’. Use these values to calculate each appropriate elasticity of demand coefficient. Briefly interpret each elasticity coefficient.
The Correct Answer and Explanation is :
Analysis of Elasticities and Demand for Chicago Bulls Tickets and Tennis Rackets
1. Interpretation of Elasticity Coefficients:
(a) Cross-Price Elasticity between Blackhawks and Bulls Tickets (4)
The cross-price elasticity (CPE) measures the responsiveness of demand for one good to a change in the price of another good. A coefficient of 4 suggests that Blackhawks tickets and Bulls tickets are strong substitutes. This means that if the price of Blackhawks tickets increases by 1%, the demand for Bulls tickets increases by 4%. Fans are likely to switch between the two depending on ticket prices.
(b) Income Elasticity for Bulls Tickets (5)
Income elasticity measures how demand responds to changes in consumer income. A coefficient of 5 indicates that Bulls tickets are a luxury good. If consumer income increases by 1%, demand for Bulls tickets rises by 5%. Conversely, a decrease in income leads to a more significant drop in ticket demand, meaning demand is highly sensitive to income changes.
(c) Cross-Price Elasticity between Bulls Tickets and United Center Parking (-8)
A negative cross-price elasticity (-8) means that Bulls tickets and parking are complements. If ticket prices rise, demand for parking drops significantly. Specifically, a 1% increase in ticket prices reduces parking demand by 8%. This makes sense since fans need parking when they attend games, and fewer attendees mean lower parking usage.
2. Demand Analysis for Bjorn Borg Tennis Mfg. Company
(a) Is the Tennis Racket a Normal or Inferior Good?
The demand function is:
[
Q = 200 – 2P + 3I + 0.5A
]
The income coefficient (3) is positive, meaning that when income (I) increases, demand for tennis rackets rises. This confirms that tennis rackets are a normal good because higher incomes lead to more purchases.
(b) Impact of $3000 Drop in Per Capita Disposable Income
Since I is measured in thousands, a $3000 drop means I decreases by 3. The demand function’s income term is 3I, so:
[
\Delta Q = 3 \times (-3) = -9
]
This means that the firm’s sales will decrease by 9 rackets per month due to the drop in disposable income.
3. Calculating Demand and Elasticities
Given:
- ( P = 75 )
- ( I = 10 ) (i.e., $10,000)
- ( A = 6 ) (i.e., $6,000)
Substituting into the demand function:
[
Q = 200 – (2 \times 75) + (3 \times 10) + (0.5 \times 6)
]
[
Q = 200 – 150 + 30 + 3 = 83
]
Elasticities:
- Price Elasticity of Demand (PED)
[
PED = \left(\frac{dQ}{dP} \times \frac{P}{Q} \right) = (-2) \times \frac{75}{83} \approx -1.81
]
Interpretation: Since PED is elastic ((< -1)), demand is highly sensitive to price changes. A 1% increase in price decreases demand by 1.81%. - Income Elasticity of Demand (YED)
[
YED = \left(\frac{dQ}{dI} \times \frac{I}{Q} \right) = (3) \times \frac{10}{83} \approx 0.36
]
Interpretation: Tennis rackets are a normal good but not a luxury good since YED is positive but less than 1. A 1% increase in income raises demand by 0.36%. - Advertising Elasticity of Demand (AED)
[
AED = \left(\frac{dQ}{dA} \times \frac{A}{Q} \right) = (0.5) \times \frac{6}{83} \approx 0.036
]
Interpretation: Advertising has a very weak effect on demand. A 1% increase in advertising spending only increases sales by 0.036%.
Summary
- Bulls tickets are substitutes for Blackhawks tickets (CPE = 4).
- Bulls tickets and parking are complements (CPE = -8).
- Bulls tickets are a luxury good (YED = 5).
- Tennis rackets are a normal good (YED = 0.36).
- A $3000 income drop will reduce tennis racket sales by 9 per month.
- Tennis racket demand is elastic to price (-1.81) but weakly affected by advertising (0.036).
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