Question

 9. Application: Elasticity and hotel rooms

 The following graph input tool shows the daily demand for hotel rooms at the Triple Sevens 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)	$200 per roundtrip
Room rate at the Exhilaration Hotel and Casino, which is near the Triple Sevens	$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.

 For each of the following scenarios, begin by assuming that all demand factors are set to their original values and that Triple Sevens 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 Triple Sevens _______  from_______  rooms per night to _______  rooms per night. Therefore, the income elasticity of demand is _______ , meaning that hotel rooms at the Triple Sevens are _______ .

 If the price of a room at the Exhilaration 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 Triple Sevens _______ 

 from _______  rooms per night to _______  rooms per night. Because the cross elasticity of demand is _______ , hotel rooms at the Triple Sevens and hotel rooms at the Exhilaration are _______ .

 Triple Sevens 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 Triple Sevens is operating on the _______  portion of its demand curve.

Possible Answer

1: falls, rises

2: negative positve

3:an inferior good, a normal good

4: falls, rises

5: negative, positive

6: complements, substitute

7: decrease, increase

8: elastic, inelastic

Answer 1

Solution:

If the average household income increases from $40,000 to $60,000 per year, we expect the demand curve to shift to right (as now, at same particular price level, an individual can get more hotel rooms. Following is the diagram indicating such shift:

So, clearly the quantity of rooms demanded at the Triple Sevens rises from 300 hotel rooms per night to 320 rooms per night (you may still verify this by filling in '60' in average income blank, then see what is reported in front of quantity demanded as that will given precise answer, however the answers followed will not differ). Notice, that as the income of households has increased, the demand for hotel rooms has also increased, indicating a positive income elasticity of demand. When income elasticity of demand is positive, it means that a good is normal, meaning hotel rooms at Triple Seven are a normal good.

When price of a room at the Exhilaration decreases, all other demand factors remaining unchanged, the quantity of rooms demanded at the Triple Sevens falls from 300 hotel rooms per night to 260 rooms per night (you may still verify this by filling in '160' in room rate at Exhilaration blank, then see what is reported in front of quantity demanded as that will given precise answer, however the answers followed will not differ). Since, as the price of room at the Exhilaration decreased, the demand for rooms in Triple Sevens decreased, so the cross price elasticity is positive. When cross price elasticity of demand is positive, it means that the other good is a substitute because as price in Exhilaration decreased, the demand for hotel rooms in that hotel increased. Now, that more people stay there, and both hotels are at close proximity, fewer people stay here in Triple Sevens, meaning hotel rooms at the Exhilaration are substitute.

Total revenue = price*quantity

Initially, TR = 200*300 = $60,000

Now, with price decreased to $175, new quantity demanded = 325 hotel rooms

So, new total revenue = 175*325 = $56,875

Notice that as the price reduced, the total revenue has also reduced (or in other words, price and total revenue move in same direction), thus, Triple Sevens must be operating on the inelastic portion of its demand curve. This is because as price decreased, the quantity demanded increased but not very strongly, ultimately leading to a reduction in the total revenue. So, percentage change in quantity demanded is lower than percentage change in price.