g A firm is the only supplier of two goods, X and Y , and the demand equations for these goods are x = 76 pX and y = 50 1 2 pY , where pX and pY are the prices of X and Y , and where x and y are (respectively) the amounts of X and Y . The firm has a total joint cost function T C = 2x2 + 2xy + 3y2 + 10. Find an expression, in terms of x and y, for the firm’s profit. Determine also the values of x and y that will maximise this profit.

4. suppose that pollution in a neighborhood comes from two factories, with marginal benefit curves given by mb1 = 12 – p1 and mb2 = 8 – p2. the level of pollution in the neighborhood is given by p = p1 + p2. the government wants to limit pollution by instituting a pollution-rights market. the government’s desired level of p is 10, so it prints 10 pollution rights and offers them for sale to the firms.a)find the equilibrium selling price of a pollution right, as well as the allocation of rights (and hence pollution levels) across the two factories. b)repeat part (a) for the case where the government’s desired level of pollution equals 14. c)comment on the usefulness of a pollution rights market in achieving efficient levels of pollution abatement.