In a restaurant somewhere in Canada, a customer emits a negative consumption externality as a result of vaping, leading to health costs for nearby patrons by way of reduced air quality and possible toxins inhaled due to passive smoke. The private market demand and supply functions for vapes is given by:
QD = 90 – 2P
QS = -10 + 8P
where QD and QS are quantities demanded and supplied, respectively, and P is the private market price. Each unit of consumption of vapes generates an external cost of $4, which is not reflected in the market demand function.
(a) Calculate the equilibrium price and quantity in the absence of any government intervention.
(b) Using the marginal social benefit function, calculate the socially optimal quantity, the new seller price, and the new consumer price. (Note: The external cost should incorporate a per unit tax of $4 per vape. The seller price (price the seller receives after the tax) will be lower than the equilibrium price calculated in part (a) and the buyer price (price paid by the vape consumer) will be higher than the equilibrium price calculated in part (a)).
(c) Illustrate using a supply and demand diagram i) market equilibrium, ii) the social benefit function, iii) deadweight loss and iv) tax amount for this negative consumption externality. Clearly label the relevant areas using the calculations from parts (a) and (b).
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