Question

9. Sheila and Ivan live in an isolated valley and trade with no one but each other. They consume only apples and oranges. Sheila has an initial endowment of 6 apples and 19 oranges. Ivan has an initial endowment of 18 apples and 20 oranges. For Sheila, the two goods are perfect substitutes, one for one. For Ivan, they are perfect complements, one for one. At all Pareto efficient allocations,

a) Sheila must consume at least 15 oranges.
b) Ivan must consume 17.50 apples.
c) the slopes of the two traders’ indifference curves are the same. d) Sheila must consume at least 25 oranges.
e) None of the above.

Answer 1

Sheila has 6 apples and 19 oranges and for her, the two goods are perfect substitutes, one for one. This means that the only thing that concerns Sheila is the total quantity of 25, and anything below it will not be acceptable to her.

On the other hand, Ivan has 18 apples and 20 oranges and for him, the two goods are perfect complements, one for one. This means, for each apple, Ivan needs one orange. So, for Ivan 18 apples and 18 oranges is needed, and any trade that reduces this amount of 18 apples and 18 oranges will not be acceptable to him.

So, we can say that Sheila must consume at least 25 oranges.