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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.)

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My attempt:

Case1:

When $P_a=P_b=1$, consumer consumes 9 units of A with wage=15 dollars.

$$x_a+P_a+x_b+P_b\le 15$$

$$9*1+x_b*1\le15$$

$$x_b\le 6$$

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.

$$x_a+P_a+x_b+P_b\le 14$$

$$10*1.1+x_b*1\le14$$

$$x_b\le 3$$

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?

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