The following graph input tool shows the daily demand for hotel rooms at the Peacock Hotel and Casino in Las Vegas, Nevada. To help the hotel management better understand the market, an economist identified three primary factors that affect the demand for rooms each night. These demand factors, along with the values corresponding to the initial demand curve, are shown in the following table and alongside the graph input tool.

Demand Factor

Initial Value

Average American household income $$40,000$ per year

Roundtrip airfare from San Francisco $($SFO$)$ to Las Vegas $($LAS$)$ $$100$ per roundtrip

Room rate at the Grandiose Hotel and Casino, which is near the Peacock $$200$ per night

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.

$0$

$50$

$100$

$150$

$200$

$250$

$300$

$350$

$400$

$450$

$500$

$500$

$450$

$400$

$350$

$300$

$250$

$200$

$150$

$100$

$50$

$0$

PRICE $($Dollars per room$)$

QUANTITY $($Hotel rooms$)$

Demand

Graph Input Tool

Market for Peacock's Hotel Rooms

Price

$($Dollars per room$)$

$200$

Quantity Demanded

$($Hotel rooms per night$)$

$300$

Demand Factors

Average Income

$($Thousands of dollars$)$

$40$

Airfare from SFO to LAS

$($Dollars per roundtrip$)$

$100$

Room Rate at Grandiose

$($Dollars per night$)$

$200$

For each of the following scenarios, begin by assuming that all demand factors are set to their original values and Peacock is charging $$200$ per room per night.

If average household income increases by $50\%,$ from $$40,000$ to $$60,000$ per year, the quantity of rooms demanded at the Peacock from

rooms per night to

rooms per night. Therefore, the income elasticity of demand is $,$ meaning that hotel rooms at the Peacock are $.$

If the price of a room at the Grandiose were to decrease by $20\%,$ from $$200$ to $$160,$ while all other demand factors remain at their initial values, the quantity of rooms demanded at the Peacock from

rooms per night to

rooms per night. Because the cross$-$price elasticity of demand is $,$ hotel rooms at the Peacock and hotel rooms at the Grandiose are $.$

Peacock is debating decreasing the price of its rooms to $$175$ per night. Under the initial demand conditions, you can see that this would cause its total revenue to $.$ Decreasing the price will always have this effect on revenue when Peacock is operating on the portion of its demand curve.