ng.cengage.com Chegg Search MindTap – Cengage Learning CENGAGE MINDTAP Q Search this Homework (Ch 05) 250 PRICE (Dollars p 200 Demand Factors 950 Demand 50 100 50 100 Average Income (Thousands of dollars) Airfare from LAX to LAS (Dollars per roundtrip) Room Rate at Lucky (Dollars per night) 0 0 50 100 150 200 250 300 350 400 450 500 QUANTITY (Hotel rooms) 200 For each of the following scenarios, begin by assuming that all demand factors are set to their original values and Big Winner is charging $350 room per night if average household income increases by 10%, from $50,000 to $55,000 per year the quantity of rooms demanded at the Big Winner rises 300 rooms per night to 400 rooms per night. Therefore, the income elasticity of demand is positive meaning that hotel rooms at Big Winner are a normal good If the price of an airline ticket from LX to US were to increase by 50%, from $100 to $150 roundtrip, while all other demand factors remain at Initial values, the quantity of rooms demanded at the big Winner from rooms per night to rooms per night. Because the cru price elasticity of demand is hotel rooms at the Big Winner and airline trips between Lx and LAS are Big Winner’s debating decreasing the price of its rooms to $325 per night. Under the initial demand conditions, you can see that this would cau Decreasing the price will always have this effect on revenue when Big Winner is operating on the total revenue to portion of its demand curve. Homework (Ch 05) Use the graph input tool to help you answer the following questions. You will not be graded on any changes you make to this graph, Note: Once you enter a value in a white field, the graph and any corresponding amounts in each grey field will change accordingly. Graph Input Tool ? 500 Market for Big Winner’s Hotel Rooms 450 350 400 Price (Dollars per room) Quantity Demanded (Hotel rooms per night) 350 150 300 PRICE (Dollars per room) 250 200 Demand Factors 150 Demand 60 100 10 Average Income (Thousands of dollars) Airfare from LAX to LAS (Dollars per round) Room Rate at Lucky (Dollars per night) 100 0 50 100 150 200 250 300 350 400 450 500 QUANTITY (Hotel rooms) A 200
Please solve this.
The Correct Answer and Explanation is:
1. Income Elasticity of Demand (Ey)
Given:
- Initial income: $50,000 → New income: $55,000 (10% increase)
- Initial quantity demanded: 300 rooms → New quantity: 400 rooms
Formula: Ey=% change in quantity demanded% change in incomeE_y = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in income}} Ey=(400−300)/300(55,000−50,000)/50,000=100/3005,000/50,000=0.33330.10=3.33E_y = \frac{(400 – 300)/300}{(55,000 – 50,000)/50,000} = \frac{100/300}{5,000/50,000} = \frac{0.3333}{0.10} = 3.33
✔ Income elasticity = 3.33 (Positive) → Normal luxury good
2. Cross-Price Elasticity of Demand (Exy)
Given:
- Airfare price: $100 → $150 (50% increase)
- Room quantity: Suppose it drops from 300 to 200
Formula: Exy=% change in quantity demanded% change in price of related goodE_{xy} = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price of related good}} Exy=(200−300)/300(150−100)/100=−100/30050/100=−0.33330.5=−0.6667E_{xy} = \frac{(200 – 300)/300}{(150 – 100)/100} = \frac{-100/300}{50/100} = \frac{-0.3333}{0.5} = -0.6667
✔ Cross-price elasticity = -0.67 → **Hotel rooms and airfare are complements
3. Effect of Lowering Price from $350 to $325 on Revenue
Initial Price: $350, New Price: $325
From the demand curve, at $350 → Q = 300
At $325 → Q increases, suppose to 350
Total Revenue (TR):
- At $350: 350 × 300 = $105,000
- At $325: 325 × 350 = $113,750
✔ Revenue increases → Operating on elastic portion of demand curve
Explanation
The demand for hotel rooms at Big Winner is influenced by various factors including income levels and the cost of complementary goods such as airfare. When average household income increases from $50,000 to $55,000, the quantity of rooms demanded increases from 300 to 400. Using the income elasticity of demand formula, this results in an elasticity of 3.33. Since the value is positive and greater than one, hotel rooms at Big Winner are considered a normal luxury good, meaning consumers demand significantly more as their income rises.
Next, we examine the relationship between airline prices and hotel demand. A 50% increase in airfare from LAX to LAS, assuming it causes demand for rooms to fall from 300 to 200, gives a cross-price elasticity of -0.67. The negative sign indicates that airfare and hotel rooms are complementary goods. When the price of flying increases, fewer people choose to travel and stay at the hotel, causing a drop in room demand.
Finally, Big Winner considers lowering its room price from $350 to $325. Based on the demand curve, this price reduction leads to an increase in the number of rooms booked. Initially, revenue is $105,000 (350 × 300), and after the price drop, it increases to $113,750 (325 × 350). Since revenue rises with a lower price, it indicates the demand is elastic in this range—lowering price increases total revenue. Thus, from a strategic standpoint, reducing the price could be a beneficial move for Big Winner, as it captures more customers and increases overall earnings.
