(12 points) Jacob produces snowboards with a technology that can be represented by the production function . The price of capital is $10 per unit and the price of labor is $5 per unit. Originally he is using 16 units of capital and 4 units of labor. How many snowboards does he produce? What is his cost of production, and what does he spend on capital? What is his optimal cost minimizing input mix for the output you found in part a? (12 points) Finals have just ended, and you have two options for how to celebrate. You can go to a local coffee shop, the Blue Fox, and drink frosty chocolate milkshakes, B, for a price of , or instead you can go to a local box social and consume ice cream cones, . Ice cream cones cost each. You can participate in both activities but have limited income. Find both marginal utilities and explain what the marginal utility of hot chocolate, B, means in terms a non-economist would understand. Write the equal marginal principle and explain what it means in terms a non-economist would understand (explain it as more than just the slope of some silly curve that most people haven’t heard of). Solve for the demand function for ice cream. (18 points) You have been hired as an analyst examining the mining industry. A new mineral, unobtanium, is discovered in only two locations on Earth, each owned by a different firm. It is a vital part of producing infant pacifiers, and has the interesting trait of often disappearing when needed. Unobtanium is the exact same regardless of where it is produced. Both firms face the market demand curve And both firms have a constant marginal cost of 25. Assume the firms compete in a Cournot fashion. Derive firm 1’s optimal response as a function of whatever quantity firm 2 will choose. Find Firm 2’s optimal response curve using symmetry Solve for both firm’s individual quantities, as well as the market quantity and price Examining your best response functions, explain why the firms would struggle to collude. Derive the perfect competition price and quantity. Is demand more or less elastic at the perfect competition price or the Cournot duopoly price? Assume that firm 1 is now able to move first. Is there a first mover advantage? Explain how you know this referring to the first mover’s optimization problem. What would happen if the two firms instead competed by choosing price? (12 points) Climate change is going to negatively impact most of the planet and is primarily caused by the emission of and other greenhouse gasses during human economic activity. You are asked to design a market-based mechanism to reduce emissions. In 1-2 sentences each, explain two of the market-based mechanisms we discussed in class for correcting an externality (no good economist provides only one option). What policy instrument is most appropriate if we know that the Earth can only tolerate some maximum quantity of pollution? Explain your reasoning in a sentence. (16 points) Assume you run a local pizza place, and are considering whether or not to expand your business. You have had several good years (your peanut butter and banana pizza has done particularly well after Ref. 64 passed). If you decide to expand, you can expect to make $600 thousand in profit, due to the cost of building new locations and hiring new staff. If you decide not to expand, profits will remain at $800 thousand. However, your success has also attracted the attention of a potential competitor. If this firm enters and you decide to expand you will only make $100 thousand in profit while your competitor will make -$100 thousand after their costs of entry. If you decide not to expand, you will make $400 thousand and your competitor will make $200 thousand by stealing your business with their cheap imitations of your recipes (their banana and peanut butter pizza is an abomination).

Read ALL directions before beginning.

• Keep written answers brief, clear and to the point. Points will be taken away for irrelevant statements.
• If you are unsure of the next mathematical steps, write the definitions you would use for partial credit.

Below several formulas are provided. They should look familiar. You may not need all of them.

Bring the exponent down front and subtract 1 from it

Partial derivative = everything else is a constant

Answer each question to the best of your ability and clearly show your work. Label all parts of any diagrams or models that are missing labels. Partial credit will not be given without work. Points will be deducted for rambling answers or incorrect information.

1. (12 points) Jacob produces snowboards with a technology that can be represented by the production function . The price of capital is $10 per unit and the price of labor is $5 per unit.
   1. Originally he is using 16 units of capital and 4 units of labor. How many snowboards does he produce?
   2. What is his cost of production, and what does he spend on capital?
   3. What is his optimal cost minimizing input mix for the output you found in part a?
2. (12 points) Finals have just ended, and you have two options for how to celebrate. You can go to a local coffee shop, the Blue Fox, and drink frosty chocolate milkshakes, B, for a price of , or instead you can go to a local box social and consume ice cream cones, . Ice cream cones cost each. You can participate in both activities but have limited income.
   1. Find both marginal utilities and explain what the marginal utility of hot chocolate, B, means in terms a non-economist would understand.
   2. Write the equal marginal principle and explain what it means in terms a non-economist would understand (explain it as more than just the slope of some silly curve that most people haven’t heard of).
   3. Solve for the demand function for ice cream.
3. (18 points) You have been hired as an analyst examining the mining industry. A new mineral, unobtanium, is discovered in only two locations on Earth, each owned by a different firm. It is a vital part of producing infant pacifiers, and has the interesting trait of often disappearing when needed. Unobtanium is the exact same regardless of where it is produced. Both firms face the market demand curve

And both firms have a constant marginal cost of 25. Assume the firms compete in a Cournot fashion.

• 1. Derive firm 1’s optimal response as a function of whatever quantity firm 2 will choose. Find Firm 2’s optimal response curve using symmetry
  2. Solve for both firm’s individual quantities, as well as the market quantity and price
  3. Examining your best response functions, explain why the firms would struggle to collude.
  4. Derive the perfect competition price and quantity. Is demand more or less elastic at the perfect competition price or the Cournot duopoly price?

Assume that firm 1 is now able to move first.

• 1. Is there a first mover advantage? Explain how you know this referring to the first mover’s optimization problem.
  2. What would happen if the two firms instead competed by choosing price?

1. (12 points) Climate change is going to negatively impact most of the planet and is primarily caused by the emission of and other greenhouse gasses during human economic activity. You are asked to design a market-based mechanism to reduce emissions.
   1. In 1-2 sentences each, explain two of the market-based mechanisms we discussed in class for correcting an externality (no good economist provides only one option).
   2. What policy instrument is most appropriate if we know that the Earth can only tolerate some maximum quantity of pollution? Explain your reasoning in a sentence.
2. (16 points) Assume you run a local pizza place, and are considering whether or not to expand your business. You have had several good years (your peanut butter and banana pizza has done particularly well after Ref. 64 passed). If you decide to expand, you can expect to make $600 thousand in profit, due to the cost of building new locations and hiring new staff. If you decide not to expand, profits will remain at $800 thousand. However, your success has also attracted the attention of a potential competitor. If this firm enters and you decide to expand you will only make $100 thousand in profit while your competitor will make -$100 thousand after their costs of entry. If you decide not to expand, you will make $400 thousand and your competitor will make $200 thousand by stealing your business with their cheap imitations of your recipes (their banana and peanut butter pizza is an abomination).

The following table shows the firms’ profits for each outcome.

• 1. Find the Nash equilibrium and write each firm’s actions below.
  2. Pick an outcome that is not a Nash, and explain why it is not – make sure to use the definition of Nash equilibrium
  3. Is “don’t expand” a dominant strategy for Firm 1? Explain why or why not.
  4. Fill in the missing payoffs in the figure below and find any Nash equilibria. How does the game change when you are able to move first?
  5. Would it be a credible threat for firm 2 to say it always enters? Explain why.

1. (12 points) You decide to take a trip to Hawaii over summer break. Your food budget is limited to two items – pineapple flavored ice cream, and kiwis purchased from a roadside stand. You have done your due diligence and found the price of both items and found your optimal combination of ice cream and kiwis. Once you arrive in Hawaii, you find that the price of kiwis has fallen since you performed your research.
2. Explain the income effect of this price change
3. Explain the substitution effect of this price change.
4. Add another budget curve to the figure below, and label both the substitution and income effects.

\

1. Is it possible that you will eat more of both foods? Why?
2. (10 points) A stranger walks up to you in the street. You have $50 in your pocket, and they say that with some probability they are going to give you $100. They are kind enough to provide you probabilities for the two potential outcomes (Leave with $50 or leave with $150), and you calculate your expected value of this “game” is $75.
3. The adrenaline overwhelmed you in the moment. Calculate the probability of gaining $100 necessary to have an expected value of $75, assuming you start with $50.
4. Assume your utility function is actually given by the figure below (this is not a graph of ). Label the expected utility of wealth, and your utility of expected wealth. Draw the risk premium on the figure below. Explain what it means in a sentence.

1. (10 points) Consider the following situation. In a population of 300 million people, there are two “types” of people. Type H (healthy), and Type S (sick). 90% of the people are healthy (Type H), and have a 1% chance of getting sick. The remainder are Type S and have a 15% chance of getting sick. Getting sick costs $200,000. Type H people are willing to pay $4,000 for insurance that covers their cost of illness. Type S people are willing to pay $22,000 to cover their cost of illness.
   1. What is the expected cost of illness for a Type S person? Are they willing to buy insurance?
   2. What is the expected cost of illness for a Type H person? Are they willing to buy insurance?
   3. What is the expected cost of illness for the population as a whole?
   4. If insurance companies could not distinguish who is healthy or who is sick, and can only charge one price for insurance, what would we expect to happen?