Question

Analyze a simple model of a consumer's response to a price increase.

% change (growth rate) = (value_new - value_old) / value_old Elasticity = |% change in quantity / % change in price|

Gasoline
	Year 1	Year 2
Price	$1.74	$2.67
Quantity	1,558.55	743.54

a. For the following questions, assume that the Year 2 price increases by an additional 30%.What would be the new Year 2 price after the additional price increase? Answer

b. Given the previously calculated price elasticity of demand, what quantity would the consumer purchase in Year 2 after the price increase? Answer

c. What would be the consumer's expenditure in Year 2 after the price increase? Answer

d. What is the change in the consumer's expenditure between Year 1 and Year 2 by Answer

e. Would a tax on this good be relatively more effective at raising revenue, or changing behavior? AnswerChanging BehaviorRaising RevenueBoth

Answer 1

a)
	Year1	Year2	Year2'
Price	1.74	2.67	3.471
Quantity	1558.55	743.54
Price (P2') =P2*(1+0.3)
P2' = 2.67*(1+0.3) = 3.471
b) elasticity =2.67* (743.54-1558.55)/(2.67-1.74)*743.54
	` = -3.15
	e =P2' (Q2' -Q1) /(P2' - P1)*Q2'
	`-3.15 = 3.471*(Q2' - 1558.55)/(3.471 - 1.74)*Q2'
	`-3.15*(1.731)*Q2' = 3.471*Q2' - 1558.55*3.471
	`-5.45Q2' = 3.471Q2' -5409.73
	5409.73 = 8.92Q2'
	Q2' '= 5409.73/8.92
	Q2' = 606.47
c) Expenditure in Year 2: E2' = P2'*Q2'
	`= 3.471*606.47
	`=2105.06
d)change in expenditure between year 1 and year2'
Expenditure in Year 1 = P1*Q1 = 1.74*1558.55
E1 = 2711.877
change = E2' - E1
` = 2105.06 2711.877
`= 606.82
e) Tax would increase price and would therefore lead to a high change in quantity
since the good is elastic Prie elasticity >-1
This imply that even a slight change in the prices will reduce the
quantity demanded by more than proportionately.
Thus a tax maynot raise revenue but a changing behavious.
Thus answer is changing behaviour.]