Intermediate Microeconomic Theory

1. (25 points) Vance refrigeration has a monopoly on the market for refrigerators in Scranton.

It has two different plants it can choose to produce from:

MC1 = 20 + 3q1

MC2 = 10 + 6q2

where qi is daily output from plant i. Vance refrigeration faces inverse demand

P = (770=3) – 3Q

Where Q = q1 + q2.

You are Bob Vance, Vance refrigeration, find the profit maximizing firm output, in the

two plants, and market price.

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ECON 3070-030 Intermediate Microeconomic Theory December 16, 2018

2. (25 points) Among Creed Bratton’s various likes and dislikes, he has acquired a particular

preference for scuba diving (if he can’t scuba, then what’s he building towards?1) and

consuming sprouted mung beans (very nutritious but they smell like death). His preferences can be represented using a minimum consumption requirement utility function as

follows:

U(s; m) = (s – s¯)1=3m2=3

Where s present hours Creed spends scuba diving and m units of sprouted mung beans

consumed. ¯ s represents the minimum amount of hours Creed must spend scuba diving

to remain sane (any less and he goes on a strangling spree). Let the price of s and m be

ps and pm respectively, Creed makes income I from his small time fake ID operation he

runs out of his car.

Find Creed’s demand for scuba diving and sprouted mung beans in terms of exogenous

variables.

1for more information, see www.creedthoughts.gov.www/creedthoughts

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ECON 3070-030 Intermediate Microeconomic Theory December 16, 2018

3. (25 points) Consider the following payoff matrix for a contest between Jim and Dwight:

Dwight (Player 2)

Front defense Back defense

Jim (Player 1) Front attack

7; 3 | 5; 10 |

3; 8 | 9; 6 |

Back attack In the above game, find the Nash equilibrium in mixed strategies. How does this equilibrium change when Dwight moves first?

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ECON 3070-030 Intermediate Microeconomic Theory December 16, 2018

4. (25 points) Stackelberg duopolists, Pizza by Alfredo and Alfredo’s Pizza Cafe both face

inverse market demand

P = 50 – Q

Even though Alfredo’s Pizza Cafe serves the best pizza in Scranton, while Pizza by Alfredo serves hot circles of garbage, they both have marginal cost MC = 20.

Find the Stackelberg equilibrium when Alfredo’s Pizza Cafe acts as the leader in this

market. How much is Alfredo’s Pizza Cafe willing to pay to be the leader? (compared to

competing in simultaneous Cournot?)

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ECON 3070-030 Intermediate Microeconomic Theory December 16, 2018

5. (25 points) The market demand curve for beets (and agrotourism) in Scranton is given

by

Qd = 400 – 8P

This market is dominated by Schrute farms, with MC = 10. There also exists a competitive fringe of 100 firms, each with MCfringe = 10 + 50q, where q is the output of one

fringe firm.

Find the profit maximizing quantity Schrute farms would produce, the resulting market

price, and the fringe’s market share.

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ECON 3070-030 Intermediate Microeconomic Theory December 16, 2018

6. (25 points) The Dunder Mifflin paper company produce services employing the following

production function

Q(L; P) = L1=4P3=4

where L is the amount of labor hours (sales team), and P the amount of time planning/having parties for the office. Denote per unit labor wage by w and per unit party

budget by b (treat b like a per unit price for parties).

Find the demand for labor and parties as a function of output and prices. Then, evaluate

the objective function to find an expression for total cost (value function)2

2It’s been a pleasure having you all this semester, that’s what she said, see you around, cheers.

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