ECO204: Solutions to Quiz #2
1. Vronsky owns a thoroughbred horse named Frou-Frou, who is running in the next horserace.
Vronsky, whose utility function is U(W) where W stands for his wealth, has placed a bet that
Frou-Frou will win first place. There is risk involv ed in this bet: If Frou-Frou loses the race,
Vronsky will lose the money he placed on the bet. But if she wins the race, he will receive a
large amount of money for winning the bet. True, False, or Uncertain: To ensure his utility is
equal to his expected utility, Vronsky is willing to pay a positive amount of money.
The statement is uncertain: it depends on Vronsky’s risk preference.
If Vronsky is risk averse, the statement is true. Without paying the risk premium, E(U) < U, so
he is willing to pay a positive amount of money to avoid risk and ensure E(U) = U. Essentially,
he is giving up money to avoid the disutility of risk.
If Vronsky is risk neutral or risk loving, the statement is false. Risk neutral individuals already
have E(U) = U without the risk premium, so they won’t be willing to pay money. Risk loving
individuals currently experience E(U) > U, so they too would be unwilling to give up money.
Paying a positive amount of money would cause both types of individuals to experience lower
utility.
2. (10 points) Levin is the proud owner of a 1,500-hectare farm in the countryside. Each spring,
he must plow the fields before sowing his seeds. He can hire farmhands (labor) to plow the
field by hand or rent tractors (capital) to plow the field in any combination. The plowing can
be accomplished with the following production function: q (hectares plowed) = 40L + 60K.
Each farmhand costs Levin $90 each day. Renting each tractor costs Levin $120 each day.
a. (5 points) Identify the long-run cost-minimizi ng combination of farmhands (L) and tractors
(K) that Levin should use to plow the 1,500 h ectares. Use one senten ce to briefly explain
your answer.
There are several ways to solve for this pr oblem – if your method doesn’t match the method
described here, you’ll still receive credit as long as it’s consistent with the right answer.
MPL = 40, MPK = 60, w = $90, r = $120
Cost-minimization occurs where: MRTS = w/r → MPL/MPK = w/r → MPL/w = MPK/r
MPL/w = 40/90 ~ 0.44, MPK/r = 60/120 = 0.50

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