Question

Homer currently has a monopoly in Springfield with his “Mr. Plow” snow plow business, and it’s time for him to buy a new (non-returnable) truck (his last one had its tires mysteriously shot out). Barney Gumble has been considering entering the market with his “Plow King” firm, so Homer realizes that his investment decision has dynamic (strategic) consequences:

Homer will choose his truck and be a monopolist for a month.
Barney will observe Homer’s truck choice and decide whether or not to enter. They will reach some sort of quantity-equilibrium based upon past decisions.

There are two possible plows that Homer might buy. The first is a standard truck; it costs $1400/month and leads to a marginal cost of $40/driveway (gas and Homer’s time). The second possible plow is a technological marvel: it automatically clears 45 driveways each month for $3500/month and leads to a marginal cost of $40/driveway for all driveways after the first 45. Barney mortally offended Prof. John Frink (the super-plow’s inventor) at Moe’s last week, so if Barney enters, it will be with a standard plow. Formally,

CStandard(q) = 1400 + 40q
CSuper-Plow(q) = 3500 if q less than or equal to 45 CSuper-Plow(q) = 3500 + 40(q – 45) if q greater than 45

The inverse demand for driveway-clearing per month in Springfield is P = 154 – Q (Q is the sum of all firms’ output). There are two months left in the winter, and neither Homer nor Barney discounts future profits.

a) Barring strategic considerations, which plow represents the superior (more efficient) technology?

b) What sort of strategic behavior does Homer’s investment choice call to mind? What is Homer’s advantage? His possible method of commitment?

c) What is Homer’s better investment choice? Below are intermediate steps you should take.

What are the outcomes (price, quantities, profits) when Homer has a monopoly?

What are the outcomes when Barney enters regardless of Homer’s plow decision?

Construct and solve the extended-form (tree) game. Keep in mind that final

payoffs should include both of the winter’s final months.

d) Is Homer’s purchase of Frink’s super-plow predatory?

Answer 1

(1) The cost function of the standard plow is C = 1400 + 40q. This cost function is shown as the blue curve in the figure below. The cost function of the super plow is such that it is 3500 for every quantity less than or equal to 45; and after that, it is C = 3500 + 40 (45-9). This cost function is shown as the red curve in the figure below. Cost 3500 1400 ------ # Quantity Since the blue curve is always below the red curve, the standard plow represents the superior (more efficient) technology. (11) Strategic considerations will induce Homer to purchase super plow (the low efficiency machine). This is to discourage entry by Barney. Homer's advantage would be a greater profit resulting from serving the entire market. (111) Homer's better investment choice is to invest in super plow. (iv) The purchase of super plow is predatory. This is because less efficient technology is adopted only to keep competitors out of the market.