Suppose that there are two products: clothing and soda. Both Brazil and the United States produce each product. Brazil can produce 100 units of...

The PPF
(production possibility frontier) of an economy describes the maximum output that the economy
can produce. Here, only two goods, clothing (C) and soda (S), are considered. The PPF's for the
two countries, Brazil and the US, are assumed to be straight lines to keep the model simple. The
PPF line describes the possible combinations of output of the two goods, C and S. Points below
the PPF represent the situation where the economy is producing goods at less than full capacity.
Any point above the PPF represents a combined output that isn't achievable under current
production possibilities (according to resources and available labour), but might be achievable
in different conditions.

1) In the case of
Brazil, we're told it can produce 100 units of clothing per year, or 50 units of soda.
Therefore, its PPF is given by

2S + C = 100

because when
C = 0, S = 50 (so that 2S = 100), and when S = 0, C = 100. The coefficients of S and C arise
from the fact that production of C (clothing) to S...