Warmup Warmup questions provide practice with problems similar to those worked in class. You…

Warmup Warmup questions
provide practice with problems similar to those worked in class. You should
think of these as C-level questions.

1. Suppose there is a single gas station in a
rural town located on an interstate highway. Bob, the gas station owner, knows
he has two types of clients: local residents (who are less price sensitive
since they would have to travel 30 miles to the nearest competitor) and
interstate travelers (who are more price sensitive since they will be traveling
onward to more competitive markets anyhow).

Bob figures that in a regular business hour, 1 local resident drops in,
with individual demand for gasoline given by qr = 20 – 4P. He also figures that
1 interstate traveler considers stopping at his gas station in the same hour,
with individual demand given by q= = 10 – P. Bob faces a constant marginal cost
of gasoline of $2 per gallon, so his cost function is C(q) = 2Q. When entry
fees are charged, the membership period only lasts for that one purchase.

3. In this question, continue with the environment described in the
warm-up, but let qe = a – P be the demand of travelers.

(a) Suppose Bob operates his business as a single-priced monopoly.

i. (10 pts) Assuming Bob prices so that both types are in the market,
answer the same five questions required in the warm-up.

ii. (3 pts) What conditions on a must hold for both types to be in the
market?

iii. (6 pts) Interpret what it means as a increases. How does this
affect the price, the amount each group buys, and the profit? Give some
intuition for these results. 12 ECON 382 Sec 1 – Stovall – 2021 Fall 6 Monopoly

(b) Next, Bob attempts third degree price discrimination, charging a
different price to local residents (who he can distinguish, since he knows all
of them).

i. (14 pts) Answer the same five questions required in the warm-up.

ii. (2 pts) What conditions on a must hold for Bob to sell to the
travelers?

ii. (6 pts) How are local residents affected by the change in a? Explain
why this differs from the answer in the single-price monopoly.

iv. (6 pts) For which values of a will travelers pay a higher price than
residents? How does this relate to whether travelers prefer (i.e. get more
consumer surplus) 3rd degree price discrimination over single- price monopoly?