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
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Transcribed Image Text: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*Y³ ,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 (ɛ) and price elasticity of supply (5) for all levels of each variable.
Use the formula for price elasticity of demand to confirm that the parameter ɛ, 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 ß 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:
а.
Income Elasticity of Gas Demand
0.66
Price Elasticity of Gas Demand
-0.58
Avg Consumption (2013)
392 gallons
Average Price per Gallon (2013)
$3.50
Avg Income (2013)
$52,000
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.
d. We can use the previous results to better understand how the impact of this proposed gas tax will vary
across households with different income levels. Construct a table that has 4 rows that correspond to the
following average household income levels: $25,000, $50,000, $75,000, and $100,000. You should
include the following columns in your table: average annual household gasoline demand when gasoline
costs $3.50, the percentage of the household annual income spent on gasoline, the loss in consumer
surplus due to the price of gasoline rising to $4.50, and the loss of consumer surplus divided by income.
Calculate the values of each cell in your table.
Given your table in part (d), how does the impact of the price increase (due to the tax) vary over the four
income levels examined? Is this consistent with the tax being regressive, that is, does the percentage of
income spent by tax payers 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.
е.
f.
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