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2. In the following, we are going to use the microeconomic theory we have developed in class to explore the short run implications of the rise in the price of gasoline in 2022 due to various factors, including the war in Ukraine. We can use the "constant elasticity" demand function, Q = Pey, as a framework for representing the demand for gasoline. The reason it is named as such is that the exponents for the price of gasoline (P) and income (Y), denote the price elasticity of demand (e) and income elasticity of demand () for all levels of each variable. a. Use the formula for price elasticity of demand to calculate the price elasticity of demand to show that it equals the parameter &. 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 constant elasticity demand function, that is, use algebra to solve for a value for the parameter (phi) based on average annual consumption, average price per gallon, and median US 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 that is easily collected by searching the web for relevant economic studies: Income Elasticity of Gas Demand Price Elasticity of Gas Demand Avg Consumption (2018) Average Price per Gallon prewar (2022) Median US Income (2018) 0.28 -0.26 414 gallons $3.44 $63,179 Note: we are just looking for a reasonable approximation of short run 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 $3.44 to $4.70 a gallon. Evaluate that integral (your answer will be a function of Y). Please round decimals to the thousandths.

2. In the following, we are going to use the microeconomic theory we have developed in class to explore the short run implications of the rise in the price of gasoline in 2022 due to various factors, including the war in Ukraine. We can use the "constant elasticity" demand function, Q = Pey, as a framework for representing the demand for gasoline. The reason it is named as such is that the exponents for the price of gasoline (P) and income (Y), denote the price elasticity of demand (e) and income elasticity of demand () for all levels of each variable. a. Use the formula for price elasticity of demand to calculate the price elasticity of demand to show that it equals the parameter &. 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 constant elasticity demand function, that is, use algebra to solve for a value for the parameter (phi) based on average annual consumption, average price per gallon, and median US 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 that is easily collected by searching the web for relevant economic studies: Income Elasticity of Gas Demand Price Elasticity of Gas Demand Avg Consumption (2018) Average Price per Gallon prewar (2022) Median US Income (2018) 0.28 -0.26 414 gallons $3.44 $63,179 Note: we are just looking for a reasonable approximation of short run 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 $3.44 to $4.70 a gallon. Evaluate that integral (your answer will be a function of Y). Please round decimals to the thousandths.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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can you help me solve question 2. please provide a detailed explanation for all the parts. Thank you 

2. In the following, we are going to use the microeconomic theory we have developed in class to explore the short run implications of the rise in the price of gasoline in 2022 due to various factors, including the war in Ukraine. We can use the "constant elasticity" demand function, Qg opey, as a framework for representing the demand for gasoline. The reason it is named as such is that the exponents for the price of gasoline (P) and income (Y), denote the price elasticity of demand (e) and income elasticity of demand () for all levels of each variable. a. Use the formula for price elasticity of demand to calculate the price elasticity of demand to show that it equals the parameter &. 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 constant elasticity demand function, that is, use algebra to solve for a value for the parameter(phi) based on average annual consumption, average price per gallon, and median US 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 that is easily collected by searching the web for relevant economic studies: Income Elasticity of Gas Demand Price Elasticity of Gas Demand Avg Consumption (2018) Average Price per Gallon prewar (2022) Median US Income (2018) 0.28 -0.26 414 gallons $3.44 $63,179 f. Note: we are just looking for a reasonable approximation of short run 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 $3.44 to $4.70 a gallon. Evaluate that integral (your answer will be a function of Y). Please round decimals to the thousandths. d. We can use the previous results to better understand how the impact of this gas price increase will vary across households with different income levels. Construct a table that has 2 rows that correspond to the following average household income levels: $50,000 and $100,000. You should include the following columns in your table: average annual household gasoline demand when gasoline costs $3.44, the percentage of the household annual income spent on gasoline, the loss in consumer surplus due to the price of gasoline rising to $4.70, and the loss of consumer surplus divided by income. Calculate the values of each cell in your table. e. Given your table in part (d), how does the impact of the price increase vary over the four income levels examined? Is this the impact of this regressive, that is, does the percentage of income spent by consumers decrease as income increases. For which income level does the change in consumer surplus the come closest to correctly estimating our preferred measure of welfare loss (compensating variation)? In no more than two sentences, use the Slutsky equation to justify your answer.
Transcribed Image Text:2. In the following, we are going to use the microeconomic theory we have developed in class to explore the short run implications of the rise in the price of gasoline in 2022 due to various factors, including the war in Ukraine. We can use the "constant elasticity" demand function, Qg opey, as a framework for representing the demand for gasoline. The reason it is named as such is that the exponents for the price of gasoline (P) and income (Y), denote the price elasticity of demand (e) and income elasticity of demand () for all levels of each variable. a. Use the formula for price elasticity of demand to calculate the price elasticity of demand to show that it equals the parameter &. 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 constant elasticity demand function, that is, use algebra to solve for a value for the parameter(phi) based on average annual consumption, average price per gallon, and median US 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 that is easily collected by searching the web for relevant economic studies: Income Elasticity of Gas Demand Price Elasticity of Gas Demand Avg Consumption (2018) Average Price per Gallon prewar (2022) Median US Income (2018) 0.28 -0.26 414 gallons $3.44 $63,179 f. Note: we are just looking for a reasonable approximation of short run 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 $3.44 to $4.70 a gallon. Evaluate that integral (your answer will be a function of Y). Please round decimals to the thousandths. d. We can use the previous results to better understand how the impact of this gas price increase will vary across households with different income levels. Construct a table that has 2 rows that correspond to the following average household income levels: $50,000 and $100,000. You should include the following columns in your table: average annual household gasoline demand when gasoline costs $3.44, the percentage of the household annual income spent on gasoline, the loss in consumer surplus due to the price of gasoline rising to $4.70, and the loss of consumer surplus divided by income. Calculate the values of each cell in your table. e. Given your table in part (d), how does the impact of the price increase vary over the four income levels examined? Is this the impact of this regressive, that is, does the percentage of income spent by consumers decrease as income increases. For which income level does the change in consumer surplus the come closest to correctly estimating our preferred measure of welfare loss (compensating variation)? In no more than two sentences, use the Slutsky equation to justify your answer.
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