Question

The market demand for gym memberships in North Florida is given by the equation

Q D N = 1000 − 20 p,

and the market demand for gym memberships in South Florida is given by the equation

Q D S = 1200 − 40 p.

Price is measured as the monthly membership fee and quantity is measured as memberships per month. In this problem assume North Florida and South Florida are separate and independent markets.

(a) Suppose the membership fee (price) is $40 per month in each market. Calculate the number of gym memberships that are expected in equilibrium in each market.

North Florida:  memberships

South Florida:  memberships

(b) Now suppose the membership fee (price) falls to $10 per month in each market. Calculate the number of gym memberships that are expected in equilibrium in each market.

North Florida:  memberships

South Florida:  memberships

(c) Using the $10 membership fee, calculate the price-elasticity of demand at the equilibrium in each market. Use the point elasticity approach.

North Florida:

South Florida:

(d) Using the $10 membership fee, calculate the total expenditures by consumers (TE) in each market.

North Florida: $

South Florida: $

(e) Using the $10 membership fee, calculate the total consumer surplus (CS) in each market.

North Florida: $

South Florida: $

(f) We can see that when the membership fee is $10 the number of gym memberships and the total expenditures are the same in each market. However, the total consumer surplus is not the same in each market. Why? Provide an economic explanation that goes beyond the mathematics.

Answer 1