Question

Suppose there are three buyers of candy in a market: Tex, Dex, and Rex. The market demand and the individual demands of Tex, Dex, and Rex are shown in the following table.

a. Fill in the missing values.

b. Which buyer demands the least at a price of \(5? The most at a price of \)7?

c. Which buyer’s quantity demanded increases the most when the price decreases from \(7 to \)6?

d. In which direction would the market demand curve shift if Tex withdrew from the market? What would happen if Dex doubled his purchases at each possible price?

e. Suppose that at a price of \(6, the total quantity demanded increases from 19 to 38. Is this a “change in the quantity demanded” or a “change in demand?” Explain.

	Individual Quantities Demanded
Price Per Candy	Tex		Dex		Rex		Total Quantity Demanded
\)8	3	+	1	+	0	=	-
\(7	8	+	2	+	-	=	12
\)6	-	+	3	+	4	=	19
\(5	17	+	-	+	6	=	27
\)4	23	+	5	+	8	=	-

Short answer

1. Missing values in the table:-

   	Individual Quantities Demanded
   Price perCandy	Tex		Dex		Rex		Total quantity demanded
   $8	3	+	1	+	0	=	4
   $7	8	+	2	+	2	=	12
   $6	12	+	3	+	4	=	19
   $5	17	+	4	+	6	=	27
   $4	23	+	5	+	8	=	36

2. Dex demands the least quantity at a $5 price. Tex demands the most quantity at $7 price.
3. Tex increases his quantity demanded by a larger amount when the price falls to $6.
4. The market demand curve will shift backward if Tex leaves the market. If Dex doubles his quantity demanded at each price, the market demand will increase accordingly, and the demand curve will shift forward.
5. An increase in the quantity demanded at $6 means a change in demand shifters, keeping price constant. This refers to a change in the demand.

Step-by-step solution

Explanation to part (a)

The total quantity demanded is the sum of quantity demanded by Tex, Dex, and Rex. Accordingly, the missing values of quantity demanded and total quantity demanded can be calculated.

For example, at a price equal to $8, the sum of the individual demands (Tex+Dex+Rex) is 3+1+0=4 units. The total quantity demanded can be calculated in a similar way for all the other prices.

	Individual Quantities Demanded
Price perCandy	Tex		Dex		Rex		Total quantity demanded
$8	3	+	1	+	0	=	4
$7	8	+	2	+	2	=	12
$6	12	+	3	+	4	=	19
$5	17	+	4	+	6	=	27
$4	23	+	5	+	8	=	36

Explanation to part (b)

The values of quantity demanded at each price in the given table will give the highest demand and lowest demand.

• At a $5 price, Tex is demanding 17 units, Dex is demanding 4 units, and Rex is demanding 6 units. Since Dex’s demand is only 4 units of candy, the lowest among the three, he is the buyer with the least demand at a $5 price.

• At a $7 price, Tex is demanding 8 units, Dex is demanding 2 units, and Rex is demanding 2 units. Since Tex’s demand is 8 units of candy, the highest among the three, he is the buyer with the most demand at a $7 price.

Explanation to part (c)

The change in quantity demanded can be estimated by subtracting the new demand from the old demand for each individual.

Thus, the increase in quantity demanded by each individual when the price changes from $7 to $6 are as follows:

• Tex=4 units (12-8)

• Dex=1 units (3-2)

• Rex=2 units (4-2)

Thus, Tex’s quantity demand increases the most when the price changes from $7 to$6.

Explanation to part (d): Effect of reducing the number of buyers

A decrease in the number of buyers in the market leads to a fall in the market demand curve and hence a backward shift in the total demand. Thus, if Tex withdraws from the market, the market demand will not include his demand. It will only include the demand of Dex and Rex, as shown below.

	Individual Quantities Demanded
Price per Candy	Dex		Rex		Total Quantities Demanded
$8	1	+	0	=	1
$7	2	+	2	=	4
$6	3	+	4	=	7
$5	4	+	6	=	10
$4	5	+	8	=	13

Thus, the original demand curve will shift backward, showing a fall equal to the demand of Tex at each price. The diagram below shows the two market demand curves. $D_1$represents the market demand curve when Tex is not in the market and $D_2$represents the market demand curve when Tex is present.

At $6 price,

• the original demand curve $D_2$shows the 19 units (=12+3+4) as the total quantity demanded, where Tex’s demand of 12 units is included as well;

• the new demand curve $D_1$shows 7 units (=3+4) as the total quantity demanded, subtracting Tex’s demand of 12 units from the original demand curve;0

• The curve shifts backward due to a reduction in the number of buyers

Explanation to part ‘d’

If Dex doubles his purchases at each price, the market demand at each price will increase by the amount of increase in Dex’s demand at that price. This is shown below.

For example: At $8 price, the total quantity demanded was4 units when the original demand of Dex was 1 unit, Tex was 3 units, and Rex was 0 units.

As shown in the table, if the demand of Dex doubles, his demand becomes 2 units (an increase of 1 unit), and the new total quantity demanded becomes 5 units, that is, the total quantity demanded increases by 1 unit as well.

	Individual Quantities Demanded
Price per Quantity	Tex		Dex		Rex		Total Quantities Demanded
$8	3	+	2	+	0	=	5
$7	8	+	4	+	2	=	14
$6	12	+	6	+	4	=	22
$5	17	+	8	+	6	=	31
$4	23	+	10	+	8	=	41

The diagram below shows the two market demand curves. $D_2$represents the market demand curve when there is no change in the given individual quantities and $D_3$represents the market demand curve when the demand of Dex doubles at each price.

At a $6 price,

• the original demand curve $D_2$shows 19 units (=12+3+4) as the total quantity demanded, where Dex’s demand was 3 units;
• the new demand curve $D_3$shows 22 units (=12+6+4) as the total quantity demanded, where Dex’s demand increases to 6 units;
• The curve shifts forward to$D_3$due to this doubling of Dex’s demand at each price.

Explanation to part (e)

Suppose the quantity demanded increases or decreases at the same level of price. In that case, other factors or demand shifters like consumer’s taste, the number of buyers, or income (price is constant) are changing, resulting in a shift in the demand curve.

Therefore, if at a $6 price, the demand increases from 19 to 38 units, the demand curve will show a forward shift due to a change in demand.