**Problem 1. **Consider an island with Tom Hanks and Wilson, and one good - coconuts. There is NO endowment of coconuts, and to have something to eat Tom Hanks and Wilson have to work climb the palm trees and gather coconuts. In one hour, Tom Hanks can gather *w ^{TH }*and Wilson

U* _{i}*(

where *c ^{i }*is consumption of coconuts,

(a) Write down the problem of person *i *∈{*TH,W*}, if Tom Hanks and Wilson are on their own and no trade is possible.

(b) Use results from the worked example in the math revision to write the expressions for optimal choices *c ^{i}*

(c) Suppose that Tom Hanks and Wilson could trade if they wanted. Would they trade? Hint: Think about what the person who would like to buy a coconut could offer in return for the coconut bought.

(d) Given your answer what can we say about the competitive equilibrium allocation? How is it different from the allocation *c ^{TH}*

(e) Suppose now that Tom Hanks and Wilson decide to pool the coconuts they gather. Write down the aggregate resource constraint for coconuts on this island - an equation that shows how total consumption of coconuts by Tom Hanks and Wilson *c ^{TH }*+

(f) Suppose that the social welfare function of the social planner is

*W*(*U**W,U**TH*) = *φ**WU**W *+ *φ**THU**TH*

where *U ^{W }*= U(

(g) Solve the social planner’s problem using the Kuhn-Tucker theorem.

(h) Suppose that *φ ^{TH }*=

the social planner allocations *c ^{TH}_{SPP}*

1

**Note **: Problems 2 and 3 are adaptations of questions found in the Gruber textbook.

**Problem 2: **The private marginal benefit associated with a product’s consumption is *PMB *= 300 − 5*Q *and the private marginal cost associated with its production is *PMC *= 3*Q*. Furthermore, the *marginal *external damage associated with the good’s production is 2*Q*. What tax should the government impose to achieve the efficient allocation? Illustrate your answer with a diagram.

**Problem 3: **Firms *A *and *B *each currently produce 100 units of pollution. The federal government wants to reduce pollution levels. The marginal costs associated with pollution reduction are *MC _{A }*= 100 + 2

1. What is the socially optimal level of each firm’s production?

2. How much total pollution is there in the social optimum?

3. Explain why it is inefficient to give each firm an equal number of pollution permits.

4. Explain the the social optimum can be achieved if firms are given equal permits but are allowed to trade them.

5. Can the social optimum be achieved using a tax on pollution? THERE ARE MINOR MISTAKES IN THE QUESTION

Subject | Mathematics |

Due By (Pacific Time) | 02/25/2015 11:00 am |

Tutor | Rating |
---|---|

pallavi Chat Now! |
out of 1971 reviews More.. |

amosmm Chat Now! |
out of 766 reviews More.. |

PhyzKyd Chat Now! |
out of 1164 reviews More.. |

rajdeep77 Chat Now! |
out of 721 reviews More.. |

sctys Chat Now! |
out of 1600 reviews More.. |

sharadgreen Chat Now! |
out of 770 reviews More.. |

topnotcher Chat Now! |
out of 766 reviews More.. |

XXXIAO Chat Now! |
out of 680 reviews More.. |