Question

A consumer must spend all of her income on two goods (Xand Y). In each of the following scenarios, indicate whether the equilibrium consumption ofgoods Xand Ywill increase or decrease. Assume good Xis a normal good and good Yis an inferior good.

a.Income doubles.

b.Income quadruples and all prices double.

c.Income and all prices quadruple.

d.Income is halved and all prices double.

Short answer

1. When, income doubles, the consumer will consume more of Good X and consume less of Good Y .
2. When income quadruples and the price doubles, the consumer will consume more of Good X and consume less of Good.Y
3. When, income quadruples and the price quadruples, the consumer will consume more of Good X and consume less of Good Y .
4. When income is halved and all prices doubled,the consumer will consume more of Good Y than Good X

Step-by-step solution

Normal good and inferior good

If there is an increase in the consumers' income, the demand for the commodity will also increase and if the consumers' income decreases, the demand for the commodity will also decrease then the good is considered as Normal good.

If there is an increase in the consumers' income, the demand for the commodity will decrease and if the consumers' income decreases, the demand of commodity will increase, then the good is considered as Inferior good.

When income doubles

a)

Here, we consider,

Good X as Normal good.

Good Y as Inferior good.

When, income doubles, the consumer will consume more of Good X and consume less of Good Y.

When income quadruples and all prices double

b)

Use the following equation:

$\text{Net Effect}=\frac{\text{change in income}}{\text{change in price}}$

By calculation, we will get,

$\begin{array}{rcl}\text{Net Effect}& =& \frac{\text{change in income}}{\text{change in price}}\\ & =& \frac{4}{2}\\ & =& 2\\ & & \end{array}$

Hence, when income quadruples and the price doubles, the consumer will consume more of Good X and consume less of Good Y .

When income and all prices quadruples

c)

Use the following equation:

$\text{Net Effect}=\frac{\text{change in income}}{\text{change in price}}$

By calculation, we will get,

$\begin{array}{rcl}\text{Net Effect}& =& \frac{\text{change in income}}{\text{change in price}}\\ & =& \frac{4}{2}\\ & =& 2\\ & & \end{array}$

When, income quadruples and the price quadruples, the consumer will consume more of Good X and consume less of Good Y .

When income is halved and all prices double

d)

Here, we consider,

Good X as Normal good.

Good Y as Inferior good.

Therefore, when, income is halved and all prices doubled,the consumer will consume more of Good Y than Good X