Theory of Consumer Behavior — NCERT Solutions

Since preferences are monotonic, more of a good is preferred if the other good is not less. So

• $(10,10)$ is preferred to $(10,9)$ because it has the same bananas and more mangoes.
• $(10,9)$ is preferred to $(9,9)$ because it has more bananas and the same mangoes.
• Therefore, $(10,10)$ is preferred to both $(10,9)$ and $(9,9)$, and $(10,9)$ is preferred to $(9,9)$.

So the ranking is

$$(10,10) \succ (10,9) \succ (9,9).$$

No. If the friend is indifferent between $(5,6)$ and $(6,6)$, then she does not prefer the bundle with more of at least one good and no less of the other. Since $(6,6)$ has more bananas and the same mangoes as $(5,6)$, monotonic preferences would require $(6,6)$ to be preferred. So the preferences are not monotonic.

The market demand is the horizontal sum of the two consumers' demands.

Given:

• $d_1(p)=20-p$ for $p\le 20$, and $0$ for $p>20$
• $d_2(p)=30-2p$ for $p\le 15$, and $0$ for $p>15$

Now add them price-wise:

• For $p\le 15$:

$$d(p)=(20-p)+(30-2p)=50-3p$$

• For $15<p\le 20$:

consumer 2 demands 0, so
$$d(p)=20-p$$

• For $p>20$:

both demand 0, so
$$d(p)=0$$

There are 20 consumers, each with demand

$$d(p)=10-3p$$

for $p\le \frac{10}{3}$.

So market demand is 20 times the individual demand:

$$D(p)=20(10-3p)=200-60p$$

for $p\le \frac{10}{3}$.

For prices greater than $\frac{10}{3}$, each consumer demands 0, so market demand is 0.

The market demand at each price is the sum of the two consumers' demands.

• At $p=1$: $9+24=33$
• At $p=2$: $8+20=28$
• At $p=3$: $7+18=25$
• At $p=4$: $6+16=22$
• At $p=5$: $5+14=19$
• At $p=6$: $4+12=16$

So the market demand schedule is:

$$p=1: 33,\ p=2: 28,\ p=3: 25,\ p=4: 22,\ p=5: 19,\ p=6: 16$$

A normal good is a good whose demand increases when income increases and decreases when income decreases. So the demand for a normal good moves in the same direction as income.

An inferior good is a good whose demand moves in the opposite direction of income. As income rises, demand falls; as income falls, demand rises. Examples given in the chapter include low quality food items like coarse cereals.

Substitutes are goods that can be used in place of each other. If the price of one rises, demand for the other tends to rise. Examples in the chapter include tea and coffee.

Complements are goods consumed together. If the price of one complementary good rises, demand for the other tends to fall. Examples in the chapter include tea and sugar, shoes and socks, and pen and ink.

Price elasticity of demand measures how responsive demand is to a change in price. It is defined as

$$e_D=\frac{\text{percentage change in demand}}{\text{percentage change in price}}.$$

It tells us how much quantity demanded changes when price changes. If the absolute value is less than 1, demand is inelastic; if it is greater than 1, demand is elastic; and if it is equal to 1, demand is unitary elastic.

Using

$$e_D=\frac{\text{percentage change in quantity demanded}}{\text{percentage change in price}}$$

Price rises from 4 to 5, so

$$\%\Delta P=\frac{5-4}{4}\times 100=25\%$$

Quantity falls from 25 to 20, so

$$\%\Delta Q=\frac{20-25}{25}\times 100=-20\%$$

Therefore,

$$e_D=\frac{-20}{25}=-0.8$$

The book says we usually refer to the absolute value of elasticity, so the price elasticity is

$$|e_D|=0.8$$

This value is not among the printed options if any were given here; the computed answer is $0.8$.

The demand curve is

$$D(p)=10-3p$$

For a linear demand curve $q=a-bp$, elasticity is

$$e_D=-\frac{bp}{a-bp}$$

Here, $a=10$ and $b=3$. At $p=\frac{5}{3}$,

$$q=10-3\cdot\frac{5}{3}=10-5=5$$

So,

$$e_D=-\frac{3\cdot\frac{5}{3}}{5}=-\frac{5}{5}=-1$$

Taking the absolute value, the elasticity is 1.

Price elasticity of demand is

$$e_D=\frac{\%\Delta Q}{\%\Delta P}$$

Given $e_D=-0.2$ and price increases by $5\%$:

$$-0.2=\frac{\%\Delta Q}{5}$$

So,

$$\%\Delta Q=-0.2\times 5=-1\%$$

Thus, demand will go down by 1%.

Given price elasticity of demand $e_D=-0.2$, demand is inelastic because $|e_D|<1$.

If the price rises by $10\%$, the percentage fall in quantity demanded would be

$$\%\Delta Q=e_D\times \%\Delta P=-0.2\times 10=-2\%$$

So quantity demanded falls by only 2%, which is less than the 10% rise in price. For an inelastic good, the book states that when price rises, expenditure moves in the same direction as price. Therefore, expenditure on the good will increase.

A 4% decrease in price caused expenditure to increase by 2%.

From the chapter, when price falls:

• if expenditure increases, demand is price elastic;
• if expenditure decreases, demand is price inelastic;
• if expenditure is unchanged, demand is unit elastic.

Since price fell and expenditure rose, the demand must be elastic. In fact, because the percentage increase in quantity is greater than the percentage decrease in price, we have $|e_D|>1$. So demand is price elastic.