4 2 General equilibrium with production (questions)

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Microeconomics II 
Undergraduate degree in Economics 
 
Review Exercises – 4.2. General equilibrium with production 
 
Exercise 32.4. from Bergstrom and Varian’s book (2006) “Workouts in Intermediate 
Microeconomics”, pp. 393-395 
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, where “m” is the 
quantity of milk and “w” is the quantity of wheat. 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) Sketch in a graph 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 the same graph to draw 
the budget constraint that he faces in his role as a consumer if he makes the 
optimal choice of what to produce. 
b) Sketch in a graph 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 the same graph to draw 
the budget constraint 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 (production)? 
d) Sketch in a graph the budget constraint for northern farmers if free trade is 
allowed and the farmers make the right choice of what to produce. Sketch in 
another graph the budget constraint 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’ 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? Sketch in a graph the budget constraint 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? Justify your answer.