# Determine the range for the amount demanded

A consumer consumes two (and only two) goods A and B. Both goods are ìgoodî in the sense that more of either is strictly better. The consumerís preferences are well-behaved (complete, transitive, continuous, strictly convex) and do not change. You are given the following information: When the price per unit of good A is $\$$1, the price per unit of good B is \$$1, and her wealth is$\$$15, she chooses to consume 9 units of good A. When the price per unit of good A is \$$1.1, the price of good B is $\$$1, and her wealth is \$$14, she chooses to consume 10 units of good A. Suppose that the price per unit of good A is$\$$1, the price per unit of good B is \$$1, and the consumerís wealth is $\$$14. What do we know about the number of units of good B she will choose? Your answer should be expressed as a range of units possible values. Explain Briefly. (Example of a wrong answer written properly: 1 # of units of good B < 7.) ———- My attempt: Case1: When P_a=P_b=1, consumer consumes 9 units of A with wage=15 dollars.$$x_a+P_a+x_b+P_b\le 159*1+x_b*1\le15x_b\le 6$$So consumer can consume 6 units of B at most. Case2: When P_a=1.1 \ \& P_b=1, consumer consumes 10 units of A with wage=14 dollars.$$x_a+P_a+x_b+P_b\le 1410*1.1+x_b*1\le14x_b\le 3$$So consumer can consume 3 units of B at most. As it is seen, as income decreases, even if price increases, the demanded amount for good A increases. So this good is inferior good. On the other hand, as income dresses, the demand for good B decreases as well. So good b is normal good. When prices are$P_a=P_b=1$And wage is 14 If$x_a= 9$, then$x_b\le 5$If$x_a= 10$, then$x_b\le 4\$

Mysolution is stack at this point.

I could not show my answer that can be expressed as a range of units possible values.

How can I determine / show this range?