The town of Villa Música has two residents: Bach and Mozart. The town currently funds its free concert series solely through individual contributions from those residents. Each of the two residents has a utility function, which depends on the consumed quantity of a private good x and the total number of concerts c, with the form u(x,c) = 3 * In x + In c. The total number of concerts provided, c, is the sum of the concerts paid for by each of the two people: c=CB + CM where ca is the number of concerts paid for by Bach and c is the number of concerts paid for by Mozart. Both Bach and Mozart have an income of €70, and the unit price of both goods (x and c) is €1. Therefore, residents are limited to offering a number of concerts in the range [0.70]. to.
How many concerts are offered if the government does not intervene? (that is, if each resident decides individually and independently how many concerts to pay for)