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1.Consider a monopolist selling vegetable oil to two consumers (assume vegetable oil is infinitely divisible, so that the monopolist can sell any nonnegative, real quantity).
The demand function of consumer 1 is p1(q1) = 16 − 3q1. Consumer 2’s demand function is p2(q2) = 14 − 5q2.
All quantities are expressed in liters and prices in pounds. The monopolist can supply vegetable oil at no cost (it has already been produced).
a) Suppose the monopolist can distinguish the two consumers and is also able to offer them fixed-quantity packages, so that they cannot continuously choose any amount they want. What packages will
the monopolist offer to the two con- sumers (state quantities and fees)? What profit will the monopolist earn? (10 marks)
b) Suppose the monopolist can still distinguish the two consumers, but now, because of regulation, it must supply any amount of oil that the consumers choose (i.e., it cannot restrict consumers’
choice to a menu of fixed packages). Thus, the monopolist will charge each consumer a different constant price per liter of oil. Furthermore, the monopolist is not allowed to charge consumers any
fixed fees. What price will the monopolist set for each consumer? What quantities will be consumed, and what will be the monopolist’s profit? (10 marks)
c) Now suppose that the monopolist can no longer distinguish the two con- sumers, but is allowed to offer fixed packages. How can the monopolist achieve the highest profit (state quantities and
fees for each package)? What is the monopolist’s profit? (10 marks)
d) Now imagine there are 75 consumers like consumer 1 and 75 consumers like consumer 2. Continue to assume that the monopolist cannot distinguish the two consumers, but is allowed to offer fixed
packages. What are the optimal packages and profits now? [Hint: Review slides 22–25 from lecture 3. You can take as given that the general principles from slide 22 still hold. How does the analysis
on slides 23–25 change?] (10 marks)
e) Finally, let there be 50 consumers like consumer 1 and 100 consumers like consumer 2. Continue to assume that the monopolist cannot distinguish the two consumers, but is allowed to offer fixed
packages. What are the optimal packages and profits now? Has the quantity supplied to each low-willingness-to-pay type (“consumer 2”) increased or decreased relative to the case in part (d)? Why
has this happened? [See the hint in part d.] (10 marks)
Q2. Consider the following homogeneous good industry. The market demand is given by P (Q) = 80 − 5Q. Let there be a single incumbent and a single potential entrant, both of which initially have the
same production technology, characterized by constant marginal cost c = 10 and no fixed costs.
The sequence of events is as follows:
1. First, the incumbent decides whether to make an investment in a cost-reducing technology. We assume that to reduce the marginal cost by the amount k1, the incumbent must pay a cost
of (k1)2. The incumbent’s cost function is thus
C1(k1, q1) = (10 − k1)q1 + k12.
Note that the maximum possible investment is kmax = c = 10, because costs cannot
2. Next, the entrant observes k1 and decides whether or not to enter. If it enters, it must pay a sunk entry cost of F = 85. The entrant has no opportunity to invest in technology, so
that if it enters, its cost function is C2(q2) = 10q2 + 85. If the entrant does not enter, it gets a payoff of zero.
3. Finally, the active firms simultaneously decide quantities. [That is, if the entrant has chosen not to enter, only the incumbent sets a quantity (i.e., solves a monopoly problem);
if the entrant has chosen to enter, Cournot competition ensues.]
4. The chosen quantities are produced and profits reaped, by which the game ends.
a) Solve for the equilibrium quantities, prices, investment level, and profits. Does the incumbent choose to accommodate or to deter entry? (30 marks)
b) Now, solve for the equilibrium quantities, prices, investment level, and profits if the sunk entry cost is F′ = 500. How is the incumbent’s problem now different from that in part (a)? [Hint:
Use your solutions from part (a) as much as possible. Is it hard for the incumbent to keep the entrant out in this case?] (10 marks)
c) Now, solve for the equilibrium quantities, prices, investment level, and profits if the sunk entry cost is F′′ = 50. How is the incumbent’s problem now different from that in part (a)? [Hint: Use
your solutions from part (a) as much as possible. Is entry deterrence feasible now?] (10 marks)