# Deriving the demand curve from consumer equilibrium

After you have worked through this section of the learning unit, you should be able to:

• illustrate and explain how the demand curve is derived from consumer equilibrium

A consumer's equilibrium position will change if the price of a good changes.

To illustrate the impact of a change in price, we will use our example of Fiona's spending on chocolate and ice cream. We assume that the price of chocolate decreases to R2. The weighted marginal utility for chocolate at a price of R2 is added in the following table:

### Weighted Marginal Utility

 Chocolate (P = 3) Chocolate (P = 2) Ice cream (P = 5) Units MU MU/P MU/P MU MU/P 1 72 24 36 120 24 2 66 22 33 115 23 3 54 18 27 100 20 4 42 14 21 85 17 5 36 12 18 70 14 6 27 9 13,5 65 13 7 24 8 12 60 12 8 18 6 9 45 9 9 9 3 4,5 35 7

Given that Fiona still has R50, how many units of chocolate and how may units of ice cream must she buy in order to maximise her utility?

By following the same procedure as in the above example, she ends up buying seven units of chocolate and seven units of ice cream and has R1 left.

From our examples, we can then conclude the following:

• At a price of R3 for a chocolate, we saw that Fiona maximises her utility by buying five units of chocolate and seven units of ice cream.
• At a price of R2 for a chocolate, we saw that Fiona maximises her utility by buying seven units of chocolate and seven units of ice cream.

#### Activity

The table below indicates Glenda's consumption of coffee and tea. Use the table to answer the questions that follow:

 Utils Coffee Tea MU MU P (R3) MU P (R6) MU MU P (R4) 1 30 10 5 48 12 2 24 8 4 40 10 3 18 6 3 32 8 4 12 4 2 16 4 5 6 2 1 12 3

### If the price of coffee increases from R3 to R6, what is the new equilibrium position for Glenda if she spends her total income of R28?

Think again.

When the price of coffee increases from R3 to R6, Glenda will be in equilibrium at two units of coffee and four units of tea. This is because the weighted marginal utilities are the same for coffee and tea, and Glenda spends her total available income of R28.

 Utils Coffee Tea MU MU P (R3) MU P (R6) MU MU P (R4) 1 30 10 5 48 12 2 24 8 4 40 10 3 18 6 3 32 8 4 12 4 2 16 4 5 6 2 1 12 3

Think again.

When the price of coffee increases from R3 to R6, Glenda will be in equilibrium at two units of coffee and four units of tea. This is because the weighted marginal utilities are the same for coffee and tea, and Glenda spends her total available income of R28.

 Utils Coffee Tea MU MU P (R3) MU P (R6) MU MU P (R4) 1 30 10 5 48 12 2 24 8 4 40 10 3 18 6 3 32 8 4 12 4 2 16 4 5 6 2 1 12 3

Correct.

When the price of coffee increases from R3 to R6, Glenda will be in equilibrium at two units of coffee and four units of tea. This is because the weighted marginal utilities are the same for coffee and tea, and Glenda spends her total available income of R28.

 Utils Coffee Tea MU MU P (R3) MU P (R6) MU MU P (R4) 1 30 10 5 48 12 2 24 8 4 40 10 3 18 6 3 32 8 4 12 4 2 16 4 5 6 2 1 12 3

### What is the quantity of coffee demanded by Glenda at a price of R3?

4 cups of coffee

 Utils Coffee Tea MU MU P (R3) MU P (R6) MU MU P (R4) 1 30 10 5 48 12 2 24 8 4 40 10 3 18 6 3 32 8 4 12 4 2 16 4 5 6 2 1 12 3

### What is the quantity of coffee demanded by Glenda at a price of R6?

2 cups of coffee.

 Utils Coffee Tea MU MU P (R3) MU P (R6) MU MU P (R4) 1 30 10 5 48 12 2 24 8 4 40 10 3 18 6 3 32 8 4 12 4 2 16 4 5 6 2 1 12 3

### Would you agree or disagree with the following statement?

If the price of coffee increases, Glenda must purchase less coffee in order to stay in equilibrium. This indicates that there is a negative relationship between the price of coffee and the quantity demanded by Glenda, and her demand curve is downward sloping.

Correct. You should agree.

Her demand curve looks like this:

You should agree.

Her demand curve looks like this: