Funny Problem Set

Short, Medium and Long Run
Consider the “gold-farming” industry (see Problem Set 1) which we can safely assume to be perfectly
competitive. Online game players can buy virtual gold coins from “farms” that kill monsters for a living.
Aggregate demand for virtual gold coins is governed by the function
p p D 100 400 ) ( − =
where p is the price of virtual gold and D(p) is the daily amount of coins demanded at that price (in
hundreds).
There are many potential gold farmers. Setting up shop requires buying a warehouse, stocking it up with
computers, and hiring the workers/players to operate the machines. We will represent the production
technology with the function
3 / 1 6 / 1 l k g =
where g is the quantity of gold coins obtained in a day (in hundreds), k is the amount of capital
investment, and l the amount of labor hired.1 Each firm also incurs a fixed cost of 1/6 dollars per day to
pay for electricity and internet connections. The rental rate of capital is ½ dollars per day, and the wage
rate for labor is $1. Workers in these firms are hired on a daily basis, and therefore the amount of labor
can be varied daily. The amount of capital used by any firm in production cannot be varied on a daily
basis, but can be adjusted on what we call here the “intermediate run” – a month. In the long run (five
months time), in addition to adjusting the amount of capital used in production, firms can enter or exit
the industry.
a. What is the long-run equilibrium in this perfectly competitive industry? Find the long-run
equilibrium price, total quantity, and number of firms active in the industry.
Suppose that the industry is at its long-run equilibrium and there is an unexpected increase in the
demand for virtual gold coins. The new demand function is:
p p D 150 750 ) ( − =
Find out the industry’s response in
b. The short run.
c. The intermediate run.
d. The long run.
In each case, find the equilibrium price, total quantity, and number of firms active in the industry.


1 Generating an account with a “level-60 Shaman” (see article in Problem Set 1) requires the input of highly trained and
specialized labor. In this problem we consider the simpler task of earning virtual gold coins which does not require
highly trained players – hence, the necessary workers can be found in relatively abundant supply.