2b

Problem 2. A violin manufacturer and a milk producer are located next to each other. The cows of the milk producer like the sound of violins being made, to the point that every additional violin reduces the production cost of the milk producer. To be precise, the cost function of the violin and milk producers are: V2 M 2 CVP(V) = E CMP(MiV) = * 15V Where V is the number of violins produced and M the number of gallons of milk produced. Suppose every violin is sold at price py = 75 dollars and the price of every gallon of milk is pM = 3. A] Find the prot-maximizing output of violins, V", and the prot maximizing output of gallons of milk, M'. B) Find the outputs, l7 and A? that maximize the sum of the prots of both rms. Explain why this output levels constitute a Pareto Optimal. In other words, why it is not possible to Pareto-improve them. C) Since the production of violins induces a positive production externality on the milk producer, the Government may consider subsidizing the violin producer by paying her some amount 5 for each violin produced. Find what the prot-maximizing output of violins would be in this case, in terms of the subsidy amounts. D) Find the amount 5 that would make the violin producer make the Pareto Optimal amount of violins you found in B)