Final answer:
To determine the monopoly price and output, we need to set marginal revenue equal to marginal cost. The monopoly price is $25 and the monopoly output is 20 units. The socially efficient price is $49 and the socially efficient output is 8 units. The maximum amount the firm should be willing to spend on lobbying efforts to prevent price regulation is $7200.
Step-by-step explanation:
To determine the monopoly price and output, we need to find the point where marginal revenue (MR) equals marginal cost (MC). In this case, the inverse demand function is P = 65 - 2Q and the cost function is C(Q) = 25Q.
To find the monopoly price, we set MR equal to MC:
65 - 2Q = 25
Solving for Q, we get Q = 20. Substituting Q = 20 back into the inverse demand function, we find P = 65 - 2(20) = 65 - 40 = 25.
So, the monopoly price is $25 and the monopoly output is 20 units.
To find the socially efficient price and output, we need to set the price equal to the marginal cost, which occurs when Q = 8. Substituting Q = 8 into the inverse demand function, we find P = 65 - 2(8) = 65 - 16 = 49.
Therefore, the socially efficient price is $49 and the socially efficient output is 8 units.
Finally, to determine the maximum amount the firm should be willing to spend on lobbying efforts, we need to calculate the difference in profit between the monopoly and socially efficient outcomes. The difference in profit can be expressed as the difference in total revenue (TR) between the two points multiplied by the difference in the average cost (AC) at the monopoly output (20 units):
(TR_monopoly - TR_efficient) * (AC_monopoly - AC_efficient)
Substituting the values, we get (25 - 49) × (25×20 - 25×8) = -24 ×300 = -7200.
Therefore, the maximum amount the firm should be willing to spend on lobbying efforts is $7200.