The equations below represent the demand and supply curves for annual gym memberships in a city. qD= 500 − 2p, qS=0.5p − 50 Because physical activity leads to better health, the city estimates that each annual gym membership saves $30 of public spending on healthcare per year (a positive externality). a. In a graph, show the market and the socially optimal equilibria for annual gym memberships in this city. Does the market equilibrium result in under- or over-consumption of memberships? What is the deadweight loss associated with the market failure in this situation?
The equations below represent the
qD= 500 − 2p, qS=0.5p − 50
Because physical activity leads to better health, the city estimates that each annual gym
membership saves $30 of public spending on healthcare per year (a positive externality).
a. In a graph, show the market and the socially optimal equilibria for annual gym memberships in this city. Does the
b. Would you recommend this city to implement a subsidy (a negative Pigouvian tax) to correct this market failure? If so, how much would be the subsidy per unit? What would be the effects of your proposed policy on the quantity, price, and aggregate welfare?
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