**Problem 1**

Let's rewrite the story of Colleen and Bill in a way that highlights the role of relative price. Suppose that Bill and Colleen produce logs and bushels at the following rates:

Colleen | Bill | |
---|---|---|

bushels | 10 | 8 |

logs | 10 | 5 |

Suppose further that Bill and Colleen value bushels of food and logs equally, so that the price of one bushel equals the price of one log.

- Notice now that valuing bushels and logs equally, creates a situation where:
- Bill gains from trade with Colleen, but
- Colleen doesn't gain from trade with Bill.
- However, she doesn't lose by trading with Bill.
- Why doesn't Colleen gain from trade?
- Leaving opportunity costs unchanged, how can the story be rewritten, so that both Bill and Colleen gain from trade?
**Hint:**How does the assumption that Bill and Colleen value bushels and logs equally prevent Colleen from gaining from trade (given the production rates above)?

**Problem 2**

Assume that there are only two countries in the world: Home and Foreign. Assume that there are 300 workers in Home and 100 workers in Foreign.

In Home, 2 units of labor are needed to produce one unit of wine and 3 units of labor are needed to produce one unit of cloth. In Foreign, 5 units of labor are needed to produce one unit of wine and 4 units of labor are needed to produce one unit of cloth.

(labor per unit of output)

Home | Foreign | |
---|---|---|

wine | 2 | 5 |

cloth | 3 | 4 |

Assume that each country's utility is given by the Cobb-Douglas function:

$$U(C,W)={C}^{0.5}\cdot {W}^{0.5}$$

Note that the demand functions associated with such a utility function are given by:

$$C({p}_{C},M)=\frac{1}{2}\cdot \frac{M}{{p}_{C}}$$

$$W({p}_{W},M)=\frac{1}{2}\cdot \frac{M}{{p}_{W}}$$

where $M$ is money income, ${p}_{C}$ is the price of cloth and ${p}_{W}$ is the price of wine.

- Find the autarky relative price of wine in each country. How much wine and cloth does each country consume in autarky?
- Now assume that Home and Foreign engage in trade. Set world relative supply of wine equal to world relative demand for wine and solve for the world relative price of wine. (Hint: assume a particular pattern of specialization).
- Are Home and Foreign better off with free trade? Discuss.

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