Gains from Exchange – Chpt 2
1. A Simple Model of Exchange (2 people or 2 countries)
a. The One-person model
i. Looking at Tradeoffs and Opportunity Costs
ii. The Farmer
1. Simplifying assumption
a. 1 person, can allocate his time to produce either meat or
potatoes, or many combinations of the two goods (per day 8
ozs or 32 ozs potatoes)
b. Assume that there is always a “constant” or linear tradeoff
between increasing production of 1 good an reducing
production of other, e.g., 32 oz potatoes/8ozs meat => 4:1
tradeoff => determines slope of his PPF (opp cost)
c. Doesn’t produce any other goods
b. Expanding the Model
i. The Rancher
1. Does everything better – “absolute advantage” over F in producing both
M & P(24 Meat:48 Potatoes)
a. This makes it harder (more difficult) so show that both will be
willing to trade
2. Why would he want to trade?
a. => would have to show:
i. He can get more P & M then going alone
ii. Find a price that has a lower “opp cost” than his own
and a price that F is willing to trade at(lower than F’s
opp cost)
c. Suppose that they specialize:
i. each produces what he is best at, nothing else, and trades
ii. Opp cost for the Rancher
1. Opp cost of producing 1 oz of potatoes = 24M/48P = -½ oz M for each oz
of potatoes
2. Opp cost of producing 1 oz meat = 48P/24M = -2 oz P for each oz of
meat produced
iii. Opp Cost for the Farmer
1. Opp cost for producing potatoes = 8M/32P = -1/4oz M for each oz of
potatoes produced
2. Opp cost of producing meat = 32P/8M = -4 P for each oz of meat
produced
iv. Who’s more efficient? (lowest opp cost of production)
1. Meat: Costs Rancher only 2 oz of P for each of M produced
a. Farmer’s costs: 4 P for each oz of M produced
2. Potatoes: Cost Farmer only 1/4 oz M for each oz of P
a. Rancher’s cost: ½ oz of M
3. Rancher: lowest cost of producing meat; Farmer lowest cost of
producing potatoes
v. What if we “specialize” and allow them to trade
1. Rancher produces only meat => 24 oz M
2. Farmer produces only potatoes => 32 oz P
vi. What would they trade at
1. Rancher’s own cost of producing 1 oz P = ½ oz M (willing to sell if he can
get > 2P for 1 M)
2. Farmer’s own cost of producing 1 oz M = 4P (willing to buy if 1 oz M
costs him < 4 oz P)
3. How about if the market price is 3P for 1M? (Both could gain)
vii. What would happen if they traded at this price?
1. Rancher starts at: (24M, 0P) => (23 M, 3P) (trades 1 oz M for 3P)
a. On his own: to get 3 ozs P = 3(-1/2) M => -1.5M => (22.5M, 3P)
2. Farmer starts at: (0M, 32P) => (1M, 29P) after trade
a. On his own: cost -4P for +1M => (1M, 28P)
viii. Greg’s example
1. Assume each would have originally produced at mid-pt of PPF
a. Farmer: (4M, 16P)
b. Rancher: (12M, 24P)
2. Rancher a) stars at (18M,12P), b) then sells 5 oz M; gets 15oz of P
a. (18M, 12P) => (13M, 27P)
b. Outside his own PPF (12M,24P) => better off
3. Farmer specializes in potatoes, i.e., produces only P; then trades 15 oz P
for 5 oz M
a. (0M, 32P) => (5M,17P)
b. Outside his own PPF (4M,16P) => better off
2. Maintained Assumptions: Effect of Changing Them
a. Only 2 people (or countries) and 2 goods => can add more of both, but harder to keep
track of graphically => have to go to equations
i. But conclusion about benefits of gains from trade remains
ii. Opportunity costs are constant
iii. Implies a linear trade-off => slope of graph (opp costs) is constant
iv. Real world: opportunity costs increase as more of the good is produced
1. “specialization of labor” => hire most productive (output per person)
first, less productive labor
2. PPF is non-linear
b. Measure slope of PPF (and hence opportunity costs) by a) constructing a tangent line to
the curve (line that touches PPF at only 1 point) and b) measuring the slope of that line