The government can use a subsidy or tax to change the profit-maximizing output for the firm. Consider that the firm will choose the output based on where MR = MC (also called MPC). Some key things to consider:

a. If the profit-maximizing output is less than the socially optimal output, then the government can institute a subsidy to encourage the firm to increase output. A subsidy will shift MR up. How much will the government need to shift MR so that MR = MC (also called MPC) at the socially optimal output?

b. If the profit-maximizing output is greater than the socially optimal output, then the government can institute a tax to encourage the firm to decrease output. A tax will increase MPC. How much will the government need to shift MPC so that MR = MPC at the socially optimal output?