Question

1) In two goods world, show that the goods must be net substitutes. If A is a gross substitute for B, show that the demand for A must be elastic.

2) Suppose there are n goods. Show that all goods cannot be net complements. Use Hicksian demand in your answer.

Answer 1

First question is answered below

1.

In two goods world, the goods must be substitutes because the consumer will always trade one good for another in case of price rise. This is because the consumer has a fixed budget, and in case the price of one good increases, it will disturb the consumer budget and he will thus have to substitute it for other good.

Demand for a good becomes elastic if there are more substitutes of it available in the market. As the number of substitute goods in the market increases, it becomes easier for the consumer to substitute it in case of price rise, making its demand elastic.