3. Suppose that a firm produces a product in amount X. There is a constant marginal cost (MC) equal to 15 , and the marginal benefit (MB) of production is given by MB=752X. But production of the good inflicts a marginal damage (MD) on other individuals according to the function MD=6+X. (a) Find the privately optimal level of production of X and the socially optimal level of production of X. (b) Find the level of pollution tax that would induce the firm to produce the socially optimal amount of X. Compute the gains or losses to all affected parties (the firm, other individuals and the government) of moving from the no-tax level of consumption to post-tax situation. (c) Devise a subsidy scheme that would induce the firm to produce the socially optimal amount of X. 3. Suppose that a firm produces a product in amount X. There is a constant marginal cost (MC) equal to 15 , and the marginal benefit (MB) of production is given by MB=752X. But production of the good inflicts a marginal damage (MD) on other individuals according to the function MD=6+X. (a) Find the privately optimal level of production of X and the socially optimal level of production of X. (b) Find the level of pollution tax that would induce the firm to produce the socially optimal amount of X. Compute the gains or losses to all affected parties (the firm, other individuals and the government) of moving from the no-tax level of consumption to post-tax situation. (c) Devise a subsidy scheme that would induce the firm to produce the socially optimal amount of X