1.

You sell homemade hot chocolate, which only needs two ingredients: milk and cocoa powder. The production function is given by h (m, c) = (min {m, c})^1/2, where m represents cups of milk, c represents tablespoons of cocoa powder and h represents cups of hot chocolate. One cup of milk costs 40 cents and one tablespoon of cocoa powder costs 10 cents. It is a perfectly competitive market with each cup of hot chocolate sold at $4. Solve for the optimal cups of hot chocolate that you should make to maximize profit.

q* =

2.

Alice and bob are deciding whether to go to the opera or the park but cannot communicate with each other. Alice prefers the park over the opera, receiving a payoff of 2 for the park and a payoff of 1 for the opera. Bob is the opposite, he would get a payoff of 2 for going to the opera and 1 from the park. But they would like to go to the same place, so Alice and Bob each get 2 additional units of utility if they end up in the same place.

Represent their moves as (Alice, Bob).

What are the (pure strategy), Nash Equilibria of this game?

_{(Select each correct answer.)}

o(Opera, Opera)

o(Park, Opera)

o(Opera, Park)

o(Park, Park)

oNone of the above

What are the dominant strategies?

_{(Select each correct answer.)}

o(Opera, Opera)

o(Park, Opera)

o(Opera, Park)

o(Park, Park)

oNone of the above

3.

Apple is deciding whether or not to invest $10,000 in research and development to develop the iGlasses. If they make this investment today, they will be able to develop the iGlasses for sure and start selling them starting from next year. They will also obtain a 10 year patent on the product. Once the patent expires, copycats will leap into the market and make it perfectly competitive. Other than the research and development investment, the cost of producing iGlasses is approximately 0. Suppose that market demand for the iGlasses is p = 200 - 5q in each year. The interest rate is 10% and there is no inflation.

Apple will...

o...develop the iGlasses

o...not develop the iGlasses

oThe answer is ambiguous.

Suppose that the U.S. Government decreases the number of years for which a patent is valid to 5.

Apple will...

o...develop the iGlasses

o...not develop the iGlass

oThe answer is ambiguous.

Following this example, how we can expect the length of patents to affect innovation?

oShorter patents will most likely increase innovation

oShorter patents will most likely decrease innovation

4.

In the US, beer and meat are the only two commodities produced and consumed. A gallon of beer requires 5 minutes of labor to produce, and a pound of meat requires 8 minutes of labor to produce. Assuyme that labor is the only input needed to produce beer and meat. There is a total of 123 billion hours of labor per year, and a total of 6.3 billion gallons of beer and 48 billion pounds of meat are produced each year in the US. Assume that wage is the same in the production of both goods, and the markets for the goods are both perfectly competitive.

Within the US under autarky, what is the ratio of the price of meat to the price of beer?

Let the ration above be . Suppose that on the international market, we can trade any amount of beer for meat or meat for beer, at a ratio of k gallons of beer to 1 pound of meat.

For what values of k will international trade increase the welfare in the US relative to autarky?

_{(Select each correct answer.)}

ok <

ok =

ok >

oNone of the above

5.

Consider a society of 100 inhabitants composed by two types of individuals. Half of them are poor and have yearly income of 10,000 dollars, and half of them are rich, with an annual income of 90,000 dollars. The government plans to tax annual income at a flat rate in order to redistribute it with a lump sum transfer T per person that is equal for all members of the society. However, for a positive tax rate of T over annual income, there is a T² leak in the bucket. Thus, for each dollar of income taxed, the total tax revenue collected is equal to T - T². Assume T 0.

Solve in terms of T and T, the total income that a rich individual has after taxed are collected and transfers are made.

Solve in terms of T and T, the total income that a rich individual has after taxes are collected and transfers are made.

Assuming that the government needs to balance the budget, solve the budget constraint of the government, and solve for the lump sum transfer T in terms of T.

To show demonstrate that you have solved these constraints, assume for a moment that T = 0.2. Given that the government needs to balance the budget, what would be T?

T =

Again assuming that T = 0.2, what would be the total income of a poor individual?

y_poor =

Again assume that T = 0.2, what would be the total income of a rich individual?

y_rich =

Now, what is the optimal tax rate T_poor that maximizes the income of a poor individual?

T_poor =

6.

Using what you found above, what is the optimal tax rate T_rich that maximizes the income of a rich individual?

T_rich =