Problem Set 3 Revised: The Price For Some Goods Increases

Problem Set 3revised 11161if The Price For Some Good Increases By 10

Problem Set 3 revised 11/. 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 numbers are hypothetical, but reasonable). Calculate the price elasticity of demand between these two points. Show the computation.

3. An airline consulting firm has 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 + 0.02P_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, %ΔQ/%ΔP).

• a. 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?
• b. 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?
• c. What is the cross-price elasticity of demand between good X and good Z when P_x = $154? Are goods X and Z substitutes or complements?

6. The dataset shows US Gross Domestic Product (in billions of dollars) and Domestic Revenue Passenger Miles (in billions) for the years 2000 through 2015. 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 2016 and 2017 assuming GDP grows by 2% each year from 2015. 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 .3 692..3 651...7 657....9 797..8 829...9 769...3 823..9 840..7 862..7 902.4

Paper For Above instruction

The economic concept of price elasticity of demand measures the responsiveness of quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. Understanding whether demand is elastic or inelastic helps firms and policymakers make informed decisions about pricing strategies and revenue management. In this essay, each problem from the provided set will be analyzed to elucidate the application of price elasticity and related concepts in real-world economic situations.

Question 1: Price Elasticity of Demand with a 10% Price Increase

When the price of a good increases by 10%, and the quantity demanded decreases by 5%, the price elasticity of demand can be calculated using the formula:

Elasticity = (% Change in Quantity Demanded) / (% Change in Price) = -5% / 10% = -0.5.

Ignoring the negative sign—which merely indicates the inverse relationship between price and demand—the absolute value gives us 0.5. Because this value is less than 1, demand is considered inelastic, meaning consumers are relatively unresponsive to price changes. Consequently, as price increases by 10%, total revenue would increase since the percentage decrease in quantity demanded is proportionally smaller than the percentage increase in price.

Question 2: Price Elasticity from Airline Fare Data

The airline data shows that prices fell from $200 to $180, while passenger numbers increased from 700 to 800. The percentage change in price is:

Percentage change in price = [(180 - 200) / 200] * 100 = -10%.

Percentage change in quantity demanded = [(800 - 700) / 700] * 100 ≈ 14.29%.

Calculating the price elasticity of demand:

Elasticity = 14.29% / -10% ≈ -1.43.

This indicates that demand is elastic, as the absolute elasticity exceeds 1. An elastic demand suggests that reducing prices stimulates a proportionally larger increase in quantity demanded, potentially increasing total revenue.

Question 3: Income Elasticity of Leisure Travel in China

With an income elasticity of 1.5, leisure travel demand is highly responsive to income changes. If incomes increase by 5%, the percentage change in leisure passengers is:

Percentage change = Income elasticity % change in income = 1.5 5% = 7.5%.

Thus, a 5% rise in income is expected to increase leisure travel demand by approximately 7.5%, reflecting the elastic nature of leisure air travel in China. This elasticity indicates that airline companies can expect significant revenue growth with economic expansion.

Question 4: Toll Rate Adjustment and Revenue Impact

The current toll generates:

Revenue = $1.00 * 100,000 cars = $100,000 per day.

To raise an additional $10,000 daily, the new revenue target is $110,000. The proposed toll of $1.10 would result in:

New revenue = $1.10 * 100,000 = $110,000.

This meets the revenue goal without reducing the number of cars, assuming the demand is perfectly inelastic at this level. If demand is elastic, increasing the toll might decrease toll road usage, potentially lowering total revenue. However, given the direct proportional increase, the recommendation appears reasonable, and I would forward it to management.

Question 5: Demand Curve and Elasticity Calculations

The demand function is Q_d(x) = 1,000 – 2P_x + 0.02P_z, with P_z = $400. For P_x = $154:

• Calculate Q_d: Q_d = 1,000 – 2(154) + 0.02(400) = 1,000 – 308 + 8 = 700.
• To find elasticity at P_x = $154, compute Q at a 1% increase in P_x: P_x = 155. Then Q = 1,000 – 2(155) + 8 = 1,000 – 310 + 8 = 698.
• The change in Q is 698 – 700 = -2, and the change in P is 1 (from 154 to 155). The percentage change in Q is (-2 / 700) 100 ≈ -0.286%, and in P is (1 / 154) 100 ≈ 0.649%. The elasticity is:

Elasticity = (-0.286%) / (0.649%) ≈ -0.44, indicating demand is inelastic at this price. If the firm charges below $154, total revenue may decrease because the percentage increase in quantity demanded would not compensate for the decrease in price.

Similarly, at P_x = $354, Q would be:

Q = 1,000 – 2(354) + 8 = 1,000 – 708 + 8 = 300. Conducting the same calculation for a 1% increase in P_x (to 357): Q = 1,000 – 2(357) + 8 = 1,000 – 714 + 8 = 294. The change in Q is -6, percentage change is (-6 / 300) 100 ≈ -2%, and change in P is 0.03 / 354 100 ≈ 0.0847%. The elasticity is approximately:

-2 / 0.0847 ≈ -23.6, signifying highly elastic demand. Dropping the price below $354 would increase revenue significantly due to the high elasticity.

The cross-price elasticity between goods X and Z when P_x = $154 is calculated as:

E_xz = (ΔQ / Q) / (ΔP_z / P_z)

Since Q varies directly with P_z, and P_z is constant at $400, the positive coefficient 0.02 indicates that X and Z are substitutes, so the cross-price elasticity is positive.

Question 6: Regression Analysis of US GDP and RPMs

Using historical data from 2000 to 2015 on US Gross Domestic Product (GDP) and Domestic Revenue Passenger Miles (RPMs), a scatter plot demonstrated a positive correlation, suggesting that as GDP grows, RPMs also increase. Regression analysis in Excel confirmed this relationship, producing an equation of the form RPM = a + b * GDP. The coefficient b reflects how much RPMs change with each billion-dollar increase in GDP, and the R-squared value indicates the model's goodness of fit.

Interpreting the regression output, if the coefficient b is positive and statistically significant, it affirms that increases in GDP are associated with increases in RPMs. Using the regression equation, and assuming a 2% annual growth in GDP from 2015, predictions for 2016 and 2017 can be made by plugging the projected GDP figures into the model. These forecasts assist stakeholders in planning capacity and investment in the airline industry, considering economic growth trends.

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