biz 12

Two farmers, Joe and Giles, graze their animals on a common land. They can choose to use the common resource lightly or heavily and the resulting strategic interaction may be described as a simultaneous-move game. The payoff matrix is the following: Joe Giles light heavy light 40, 40 20, 55 heavy 55, 20 30, 30 1. Find the Nash equilibrium of the game and show that it is an example of "Prisoners' Dilemma" games. 2. Suppose that the same game is repeated infinitely. Is the {light, light} outcome a Nash equilibrium if both players play a Grim strategy and have a discount factor of 0.7?

Distinguish simultaneous-move games and dynamic games in terms of information. Explain why in dynamic games Nash equilibria may not be subgame perfect. Using examples, show how non-credible threats are ruled out using backward induction.

Fill in the blanks to make the following statements correct a. Long-run sustained increases in potential output are called ___. b. Increases in material living standards occur with increases in real ____. c. An important cost of economic growth is the sacrifices of current ____ in exchange for investment that raises future ____. 2. a. An increase in the real interest rate leads to a(n) ____ in the amount of national saving as households reduce their ____. b. An increase in the interest rate leads firms to ____ their amount of desired investment. c. In the long run, with output equal to potential, equilibrium in the market for financial capital determines the interest rate as well as the amount of ____ and ____ in the economy. d. Following a shift in either the supply of national saving or the demand for investment, there will be a change in both the equilibrium ____ and the amount of ____ in the economy. 3. Fill in the blanks to make the following statements correct. a. An important aspect of the Neoclassical growth model is that increases in the supply of one factor, all else held constant, imply eventually ____ marginal returns to that factor. b. In the Neoclassical growth model, an increase in the labour force (with capital held constant) will ____ total output and ____ the level of per capita output. c. When a new and better harvesting machine replaces an old harvesting machine on a farm and is more productive than the old one, we say there has been ____ technical change. d. Some advanced growth theories are based on the assumption that technological change is ____ to the economic system; others are based on the possibility that there are ____ marginal returns to investment. e. Neoclassical growth theories are pessimistic because they emphasize ____ returns with a given state of ____. Advanced growth theories are more optimistic because they emphasize the unlimited potential of _____.

Donald and Andrew The Architect Andrew and the businessman Donald are negotiating a deal that Donald would hire Andrew to design a clubhouse in Donald's golf course in NY. This design would incur cost $10 to Andrew.

1. (2) Andrew needs the profit to be at least $5 to join the deal. What is the minimum price p0 for the design with which Andrew would be interested to join the deal?

2. (2) At this price they reach a deal. After Andrew designs the clubhouse and the clubhouse is built, Donald comes to Andrew and says he would like to renegotiate the price for the design. Since the clubhouse is already built, the same design cannot be used in other places. Since a lawsuit would be costly, if they settle in a lawsuit, Andrew can only get a share, 1 w, of the formerly agreed price p0, where w is a measure of the inefficiency of the legal system and 0 < w < 1. At what minimum price p1 for the design can now Donald just force Andrew to accept? Write p1 in terms of w.

3. (2) Based on your answer to the above question, understanding this potential renegotiation, will Andrew join the deal in the first place at the price p0? Why?

4. (1) The price difference p0 p1 is a measure of the severity of the hold-up problem. Write it in terms of w.

5. (2) How does the inefficiency of the legal system affect the severity of the hold-up problem? Why?

Assume that a baseball series lasts 5 games. Suppose a baseball pitcher strikes out an average of 2 players per game;

- Calculate the average number of players struck out by this pitcher per baseball series.

- Calculate the variance of players struck out by this pitcher per baseball series.

- What is the probability that this pitcher strikes out exactly 6 players over a series?