What is the own price elasticity of demand when px

Question

1. If the price for some good increases by 10% and the quantity demanded falls by 5%, (a) what is the price elasticity of demand, and (b) is this elastic or inelastic?

2. Last year the US low-cost-carrier Spirit Airlines entered the Dallas-Chicago market. The average ticket price for all airlines servicing the route fell from $200 to $180. After Spirit's entry, the number of passengers increased from 700 to 800 per day (these number are hypothetical, but reasonable). Calculate the price elasticity of demand between these two points. Show the computation.

3. An airline consulting firm as determined that the income elasticity for leisure air travel in China is 1.5. If incomes increase by 5% next year, what is the percentage change in leisure passengers expected next year? Show the computation.

4. The state operates a toll road which currently charges $1.00 per car with 100,000 cars using the road daily. The state wishes to raise an additional $10,000 per day for road maintenance. A newly hired financial analyst proposes raising the toll to $1.10 per car. The analyst reports to you. Will you accept and forward her recommendation to your boss?

5. The demand curve for a product is given by Q^d_x = 1,000 - 2P_x +.02P_z where P_z = $400. (Hint:  If you're not comfortable with the calculus alternatives, compute Q at the given prices, then again with a 1% increase in price. Then figure percentage change in Q over the percentage change in P, %?Q/%?P).

1. What is the own price elasticity of demand when P_x = $154?  Is the demand elastic or inelastic?  What would happen to the firm's revenue if it decided to charge a price below $154?
2. What is the own price elasticity of demand when P_x = $354?  Is the demand elastic or inelastic?  What would happen to the firm's revenue if it decided to charge a price below $354?
3. What is the cross-price elasticity of demand between good X and good Z when P_x = $154?  Are good X and good Z substitutes are complements? 

6. The data are real US Gross Domestic Product (in billions of dollars) and Domestic Revenue Passenger Miles (in millions) for the years 1996 through 2012. Below this table is the MS Excel Summary Output regressing RPMs against GDP. Using MS Excel or another similar application, build a scatter plot and insert the regression line and equation. Next, interpret the regression output and explain the regression statistics. Be certain that the regression coefficients match those in the scatter plot equation. Finally, use the regression equation to predict RPMs for 2013 and 2014 assuming GDP grows by 3% each year from 2012. You may wish to check the actual RPMs to see how closely your estimate matched. Note:  To build a scatter plot in Excel, select and copy the GDP and RPM data into Excel; select the data in Excel, then use Insert/Scatter to create a scatter plot. Finally, scroll down Chart Layout to select the format that creates a regression line and formula. Use the Excel Help function as needed.

Year	GDP	RPM
1996	8,100.2	419.07
1997	8,608.5	438.42
1998	9,089.1	448.58
1999	9,665.7	472.96
2000	10,289.7	500.12
2001	10,625.3	472.60
2002	10,980.2	469.96
2003	11,512.2	492.73
2004	12,277.0	542.82
2005	13,095.4	569.24
2006	13,857.9	574.52
2007	14,480.3	592.33
2008	14,720.3	568.25
2009	14,417.9	538.98
2010	14,958.3	552.85
2011	15,533.8	563.65
2012	16,244.6	568.70

 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.926457
R Square	0.858323
Adjusted R Square	0.848878
Standard Error	21.52755
Observations	17
ANOVA
	df	SS	MS	F	Significance F
Regression	1	42114.69	42114.69	90.87497	9.342E-08
Residual	15	6951.532	463.4355
Total	16	49066.22
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	275.7148	25.82438	10.67653	2.1E-08	220.6713974	330.7581059
GDP	0.019662	0.002063	9.532837	9.34E-08	0.015265596	0.02405796