We are concerned about the evolution of housing rental prices. We want to analyze the effects of regulating this market by introducing a price ceiling. Let the demand in the housing market be given by D(p) = 1000-p and the supply be S(p) = p, where p denotes price. Answer the following questions. (a) Compute the equilibrium price and quantity without regulation. (b) Suppose we introduce a price ceiling of 800 euros. How will it affect this market? Who will be better off? and worse off? Does it create an inefficiency? Carefully derive and explain. (c) Now, suppose, instead, we want to give a subsidy per apartment rented (a quantity subsidy). How much should the subsidy be for the equilibrium quantity to be the same as with a price ceiling? Carefully derive. (d) Given the subsidy you have just solved for, compare the effects of the subsidy with the effects of the price ceiling in part (b). Evaluate the implications for the two sides of the market (demand and supply) and the aggregate effects. Which of the two policies would you recommend? Carefully explain (and derive if necessary).