The Isle of Veritas has made it illegal to trade with the outside world. Only two commodities are consumed on this island, milk and wheat. On the north side of the island are 40 farms. Each of these farms can produce any combination of non-negative amounts of milk and wheat that satisfies the equation m = 60 − 6w. On the south side of the island are 60 farms. Each of these farms can produce any combination of non-negative amounts of milk and wheat that satisfies the equation m = 40 − 2w. The economy is in competitive equilibrium and 1 unit of wheat exchanges for 4 units of milk.
(a) On the diagram below, use black ink to draw the production possibility set for a typical farmer from the north side of the island. Given the equilibrium prices, will this farmer specialize in milk, specialize in wheat, or produce both goods? __________ Use blue ink to draw the budget that he faces in his role as a consumer if he makes the optimal choice of what to produce.
(b) On the diagram below, use black ink to draw the production possibility set for a typical farmer from the south side of the island. Given the equilibrium prices, will this farmer specialize in milk, specialize in wheat, or produce both goods? __________ Use blue ink to draw the budget that he faces in his role as a consumer if he makes the optimal choice of what to produce.
(c) Suppose that peaceful Viking traders discover Veritas and offer to exchange either wheat for milk or milk for wheat at an exchange rate of 1 unit of wheat for 3 units of milk. If the Isle of Veritas allows free trade with the Vikings, then this will be the new price ratio on the island. At this price ratio, would either type of farmer change his output? ________
(d) On the first of the two graphs above, use red ink to draw the budget for northern farmers if free trade is allowed and the farmers make the right choice of what to produce. On the second of the two graphs, use red ink to draw the budget for southern farmers if free trade is allowed and the farmers make the right choice of what to produce.
(e) The council of elders of Veritas will meet to vote on whether to accept the Viking offer. The elders from the north end of the island get 40 votes and the elders from the south end get 60 votes. Assuming that everyone votes in the selfish interest of his end of the island, how will the northerners vote? __________ How will the southerners vote? _________ How is it that you can make a definite answer to the last two questions without knowing anything about the farmers’s consumption preferences? _______________
(f) Suppose that instead of offering to make exchanges at the rate of 1 unit of wheat for 3 units of milk, the Vikings had offered to trade at the price of 1 unit of wheat for 1 unit of milk and vice versa. Would either type of farmer change his output? _________________ Use pencil to sketch the budget line for each kind of farmer at these prices if he makes the right production decision. How will the northerners vote now? ___________ How will the southerners vote now? __________ Explain why it is that your answer to one of the last two questions has to be “it depends.” __________