ECONOMICS OF ENVIRONMENT
Governments are often asked to tax foods or drugs which are harmful to only some people, and this assignment shows some of the difficulties involved. A hint from the marking of previous assignments is to show your working and label graphs carefully.
Suppose an individual’s private marginal benefit (also known as her Marginal Willingness to Pay) for bags of chips is as follows:
MPB=30-QD
where QD indicates number of bags of chips consumed. (hint, what is another name for marginal willingness to
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pay?)
1. (1 mark) Draw the individual’s demand curve in Q,P space, with Q on the horizontal axis.
2. (1 mark) Suppose the supply curve for chips is MPC = 2 Q.
Draw the supply curve on the same graph above as where you drew the demand curve.
3. (3 marks) Assume for now that there are no taxes and calculate the equilibrium quantity and price [1]; be sure to show your work
PNoTax=
QNoTax=
Indicate these values on your graph.
4. (2 marks) Calculate the consumer surplus and producer surplus in the chip market: CSNoTax=
PSNoTax=
5. (3 marks) In Q1-Q4 we have considered an individual for whom there are no external costs associated with chip consumption; denote this person by ZR (for “zero risk”). What is the total welfare associated with a ZR-type individual’s equilibrium chip consumption when there is no tax in place?
WZRNoTax = ________ CS +PS +TR (tax revenue)
6. (1 mark) Suppose that, for some other consumer labeled HR (for “high risk”) the external cost from their consumption is $0.50/bag. Using the graph you drew in Q1 to Q3, draw the Marginal Social Benefit (MSB) for a HR-type individuals’ chip consumption on the same graph.
7. (1 mark) Calculate total welfare associated with a HR-type individual’s equilibrium chip consumption when there is no tax in place.
WHRNoTax=_____________________
8. (3 marks) Suppose the government is worried about obesity and hyper-tension and institutes a $0.50 bag tax on chip consumption (which the consumer pays). Assuming the consumer’s price PD and the seller’s price PS are each measured in dollars, this means the following equation must hold in equilibrium: PeD=.5+PeS where PeD is the price associated with the equilibrium quantity read off the demand curve and PeS is the price associated with the equilibrium quantity read off the supply curve. Calculate the consumer price, producer price, and quantity sold/bought in equilibrium by either type of individual when there is a $0.50 tax on bags of chips. Note the tax applies to everyone, and externalities do not change behaviour, so HR and ZR individuals act the same.
Consumers’ price in presence of a tax= PD,Tax=
Producers’ price in presence of a tax = PS,Tax=
QTax=
9. (5 marks) Calculate the consumer surplus (for either type), the government’s tax revenue (TR) (for either type), the total external costs (EC)(only negative for the HR type) and the producer surplus when there is a $0.50 tax:
CSTax=
PSTax=
TRTax=
ECZRTax=
ECHRTax=
10. (3 marks) Suppose there are 5 type ZR individuals in the economy for every 5 type HR individual. Will imposing the chip tax on all individuals lower total welfare relative to the scenario in which no tax is imposed?
Total Welfare tax = Total Welfare no tax = TWno tax-TWtax =
11. (2 marks) Suppose that the original equilibrium price without any tax (calculated in Question 3) just happens to be the world price of chips, meaning that there is an infinitely elastic supply of chips available at this price from
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overseas. Discuss how effective the tax on chip consumption would be now. What do you conclude about the relationship between Pigovian taxes (taxes designed to fix externalities) and trade taxes?
[1] The superscript “NoTax” indicates the scenario in which there are no taxes imposed.