1. In the following, we are going to use the microeconomic theory we have developed in class to better understand the potential impact of a rise in the price of gasoline due to a tax increase. We can use the following "constant elasticity" demand function, Qg = Bp*y$,as a reasonable structure to assume for the demand for gasoline. The reason it is named as such is that the exponents for the price (P) and income (Y), represent the price elasticity of demand (e) and price elasticity of supply () for all levels of each variable. a. Use the formula for price elasticity of demand to confirm that the parameter &, in fact, represents this demand equation's price elasticity. Note that you would receive an analogous result if you did this for income elasticity of demand. b. Use the following estimated values to "calibrate" the demand function given above, that is find a plausible value for the parameter based on average annual consumption, average price per gallon, and average income. Once you are done calibrating, you should be able to write the demand function with numerical values for everything but Qg, P, and Y. Everything you need can be found in the following real world data collected from various economic studies: 0.66 -0.58 Income Elasticity of Gas Demand Price Elasticity of Gas Demand Avg Consumption (2013) Average Price per Gallon (2013) 392 gallons $3.50 $52,000 Avg Income (2013) Note: we are just looking for a reasonable approximation of gasoline demand here. If it was important to be more precise, we would use data to estimate the demand for gasoline without some of the assumption we are implicitly making here. C. Using the calibrated demand function you found in part (b), set up the integral that gives the change in consumer surplus when the price of gasoline rises from $3.50 to $4.50 a gallon. Evaluate that integral (your answer will be a function of Y). Please round decimals to the thousandths.
1. In the following, we are going to use the microeconomic theory we have developed in class to better understand the potential impact of a rise in the price of gasoline due to a tax increase. We can use the following "constant elasticity" demand function, Qg = Bp*y$,as a reasonable structure to assume for the demand for gasoline. The reason it is named as such is that the exponents for the price (P) and income (Y), represent the price elasticity of demand (e) and price elasticity of supply () for all levels of each variable. a. Use the formula for price elasticity of demand to confirm that the parameter &, in fact, represents this demand equation's price elasticity. Note that you would receive an analogous result if you did this for income elasticity of demand. b. Use the following estimated values to "calibrate" the demand function given above, that is find a plausible value for the parameter based on average annual consumption, average price per gallon, and average income. Once you are done calibrating, you should be able to write the demand function with numerical values for everything but Qg, P, and Y. Everything you need can be found in the following real world data collected from various economic studies: 0.66 -0.58 Income Elasticity of Gas Demand Price Elasticity of Gas Demand Avg Consumption (2013) Average Price per Gallon (2013) 392 gallons $3.50 $52,000 Avg Income (2013) Note: we are just looking for a reasonable approximation of gasoline demand here. If it was important to be more precise, we would use data to estimate the demand for gasoline without some of the assumption we are implicitly making here. C. Using the calibrated demand function you found in part (b), set up the integral that gives the change in consumer surplus when the price of gasoline rises from $3.50 to $4.50 a gallon. Evaluate that integral (your answer will be a function of Y). Please round decimals to the thousandths.
Chapter6: Demand Relationships Among Goods
Section: Chapter Questions
Problem 6.9P
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you