Question

In the following figure, a consumer is initially in equilibrium at pointC .

The consumer’s income is $\backslash (400$, and the budget line through point C is given by $\backslash )400=\backslash (100X+\backslash )200Y$ .When the consumer is given a $\$100$ gift certificate that is good only at store X , she moves to a new equilibrium at point D.

a.Determine the prices of goods X and Y

b.How many units of product Ycould be purchased at point A ?

c.How many units of product Xcould be purchased at point E?

d.How many units of product X could be purchased at point B ?

e.How many units of product Xcould be purchased at point F?

f.Based on this consumer’s preferences, rank bundles$A,B,C,D$ in order from most preferred to least preferred.

g.Is product Xa normal or an inferior good?

Short answer

1. The price of Good X is and Good Y is $\$200$.
2. The units of product that could be purchased at point A is 2 units.
3. The units of product that could be purchased at point E is 4 units.
4. The units of product that could be purchased at point B is 5 units.
5. The units of product that could be purchased at point F is 5 units.
6. Ranking the consumers preference, the most preferred bundle will be Point D , next is, Point B , then, Point C , and lastly, Point A.
7. Product X is a normal good.

Step-by-step solution

Finding the price of Good X .

a)

Use the equation:

$P_{x}X+P_{y}Y=M$

Here,

M is the price of Good X

$P_x$is the price of Good Y

M is the Consumer’s Income.

Given that the budget line through Point C is

$\$400=\$100X+\$200Y$

And, the Consumer’s income is$\$400$.

By substituting the following we will get,

$$\begin{gathered} P_{x}X+P_{y}Y=M \\ \$100X+\$200Y=\$400 \end{gathered}$$

Hence,the price ofGood X is$\$100$ and GoodYis$\$200$.

Finding the units of product that could be purchased at point  

b)

Here, point A is plotted on the vertical intercept, to determine the units of product that could be purchased at point B.

Use the formula:

$Y=\frac{M}{P_y}$

Here,

Y is the maximum quantity ofGood Y

$P_y$is the price ofGood P

M is the Consumer’s Income.

Given that the budget line through Point C is

$\$400=\$100X+\$200Y$

And, the Consumer’s income is$\$400$.

By substituting the following we will get,

$$\begin{gathered} Y=\frac{M}{P_y} \\ Y=\frac{\$400}{\$200} \\ Y=2 \end{gathered}$$

Hence, the units of product that could be purchased at pointAis 2 units.

Finding the units of product that could be purchased at point  E

c)

Here, point E is plotted on the horizontal intercept, to determine the units of product that could be purchased at point E.

Use the formula$=\frac{M}{P_x}$

Here,

$P_x$is the price ofGood X

is the Consumer’s Income.

Given that the budget line through Point C is

$\$400=\$100X+\$200Y$

And, the Consumer’s income is$\$400$.

By substituting the following we will get,

$$\begin{gathered} \frac{M}{P_x} \\ =\frac{\$400}{\$100} \\ =4 \end{gathered}$$

Hence, the units of product that could be purchased at pointEis4units.

Finding the units of product that could be purchased at point  

d)

Here, the consumer is given a$\$100$gift certificate that is good only for Store X .

Given that the consumer's income is$\$400$ , and an additional$\$100$gift certificate, that caused it to move to a new equilibrium at Point D , which means that the consumer can purchaseworth at Store X .

Now, to determine the units of product that could be purchased at point B .

Use the formula$=\frac{M}{P_x}$

Here,

$P_x$is the price ofGood X

M is the Consumer’s Income.

Given that the budget line through Point C is

$\$400=\$100X+\$200Y$

And, the Consumer’s income is$\$500$.

By substituting the following we will get,

$$\begin{gathered} \frac{M}{P_x} \\ =\frac{\$500}{\$100} \\ =5 \end{gathered}$$

Hence, the units of product that could be purchased at pointBis 5 units.

Finding the units of product that could be purchased at point  

e)

Here also, the consumer is given a$\$100$gift certificate that is good only for Store X .

Given that the consumer's income is$\$400$, and an additional$\$100$gift certificate, that caused it to move to a new equilibrium at Point D , which means that the consumer can purchase$\$500$worth at Store X .

Now, to determine the units of product that could be purchased at point F .

Use the formula$=\frac{M}{P_x}$

Here,

$P_x$is the price ofGood X

M is the Consumer’s Income.

Given that the budget line through Point C is

$\$400=\$100X+\$200Y$

And, the Consumer’s income is$\$500$.

By substituting the following we will get,

$$\begin{gathered} \frac{M}{P_5} \\ =\frac{\$500}{\$100} \\ =5 \end{gathered}$$

Hence, the units of product that could be purchased at point F is 5 units.

Finding the rankings:

f)

The consumer's main aim is to choose the best consumption bundle that can satisfy his or her expectations.

As per the above calculations and the diagram, since point D is at the higher indifference curve, it is more likely to be chosen by the consumer to be his or her more preferred consumption bundle.

Hence, we can say, Ranking the consumers preference, the most preferred bundle will be Point D , next is, Point B , then, Point C , and lastly, Point A. X

Finding whether the product X  is a normal or an inferior good

g)

As per the above calculations and diagrams, we can easily say Product X is a normal good.

Normal Good is a good that when an increase in the consumer's income happens, there will be an increase in its demand.

Since, the consumers income increases, the demand for Product X also increases.