COURSE: MICROECONOMICS 2

On a beach there are 3 independent businesses: Food [A], Balloons [G] and Sea Equipment Rental [E]. Each with its own cost in dollars (US$): C_i(q_i) = 1,000 + 5q_i + q_i²/4; where i = A, G, E Demand function for each company is: D_A(p_A) = 100 - p_A D_G(p_G) = 100 - p_G/2 D_E(p_E) = 100 - p_E/4 In addition, business owners have possibility of hiring a concert by a "salsa" band that charges US$ 1,000 per hour. Concert benefits businesses as follows: f(h_A) = 40 h f(h_G) = 50 h f(h_E) = 110 h And cost of presenters is: C(h) = 500*h², where h is variable for number of active hours. Answers: (a) Beach businesses decide not to hire concert (and it is held elsewhere). What is quantity demanded, profits, and price for each business? Answer mathematically. (b) Assume now that businesses want to calculate social optimum provided by concert business if it were at beach. What are new optimal quantities, profits, and prices of both concert business and entertainment businesses? (c) Suppose a vote is taken and everyone must pay one-third (1/3) of additional concert cost of playing 20 minutes longer (and a $100 travel expense), who would be in favor and who would not (suppose everyone pays 1/3 of cost)? Is this decision optimal?