Question

Now suppose the monopolist has a positive fixed cost ? which is less than the variable profit he would make as an unregulated monopolist (i.e., without regulation, he makes a positive profit). However, with regulation, he has the option to shut down to forgo ?. Clearly it is bad for the regulator if the monopolist shuts down, so the regulator must be careful to avoid such a scenario.

(c) This dilemma creates something called an Individual Rationality (IR) constraint which states that (?−?)?≥?. This modifies the regulator’s problem from part (b); the objective function is the same, but now there is a constraint. Show that the IR constraint binds by setting up the Lagrangian and taking first order conditions. You do not have to solve for the price.

(Note that, if the constraint doesn’t bind, then the Lagrange multiplier on the IR constraint, ?, is zero. Find the contradiction in the FOCs to show ?=0 cannot be the case.)

[From Part (b) -- consumer surplus is just 12?(10−?); total surplus is (?−?+12(10−?))(10−?)=(?2+5−?)(10−?); price ? set to maximize social surplus; Answer to Part (b) __  2p2-20p-(5+c) = 0]

Answer 1