Q. In a certain city where all parking is controlled by the city, it is possible to provide parking facilities in the downtown area at a constant marginal capital investment of $10,000 per space. Costs of operation can by neglect. There are three equal periods during the day of 8hrs each also spaces are rented only for complete eight hour periods. During the peak period of each of 250 days every year demand for parking is given by P= a-bQ, where P is the price per period for a space of parking. Through the other 2 off peak periods of those 250 days, the spaces demanded are half that in peak time for every possible price. On other days demand is zero. Assume that the interest rate is 10 percent and the facilities do not depreciate.

If a=$16, b= 0.08, and existing spaces are 120, Illustrate what would be the socially optimal prices during the three periods? Illustrate what would be the most optimal number of spaces, and Illustrate what are these corresponding prices?