Final answer:
The monopoly price is 46 and the monopoly output is 4 units. The socially efficient price is 47 and the socially efficient output is 3 units. The maximum amount the firm should be willing to spend on lobbying efforts is the difference in profit between the monopoly level and the socially efficient level.
Step-by-step explanation:
The monopoly price can be determined by setting the marginal revenue (MR) equal to the marginal cost (MC). In this case, MR = P, so we set P = MC. The marginal cost is given by the cost function C(Q) = 18Q. By substituting P = MC into the inverse demand function P = 50 - 1Q, we get 50 - 1Q = 18Q. Solving for Q, we find Q = 4. The monopoly price is obtained by substituting Q into the inverse demand function, giving P = 50 - 1(4) = 46.
The monopoly output is Q = 4 units.
The socially efficient price is determined by setting the marginal cost equal to the marginal benefit, which is equal to the demand curve at the socially efficient level of output. In this case, MC = 18Q and the demand curve is given by P = 50 - 1Q. By setting MC = P, we find that 18Q = 50 - 1Q. Solving for Q, we get Q = 3. The socially efficient price is obtained by substituting Q into the demand curve, giving P = 50 - 1(3) = 47.
The socially efficient output is Q = 3 units.
To prevent the price from being regulated at the socially optimal level, the firm should be willing to spend up to the amount by which its profit at the monopoly level exceeds its profit at the socially efficient level. The profit at the monopoly level is given by (P - MC)Q, where P = 46, MC = 18Q, and Q = 4. The profit at the socially efficient level is given by (P - MC)Q, where P = 47, MC = 18Q, and Q = 3. Therefore, the maximum amount the firm should be willing to spend on lobbying efforts is (P - MC)Q at the monopoly level minus (P - MC)Q at the socially efficient level.