Question

3. Suppose that a consumer with income of birr 90 wants to spend the whole income on good B and good A. Assume that the goods are consumed on a one-to-one basis and one good is worthless without the other. The price of good A and B are both 3 birrs.

i. How many units of good A&B will the consumer buy?

ii. If the price of good A increases to birr 6, how many he/she buy of each?

iii. What type of preferences does consumption of the two goods represent? What is the shape of the indifference curve for this type of preference?

Answer 1

I) Income M = $90$

Quantities $A \space and \space B$

M = Q_aP_a+ Q_bP_b

$Qa = \frac{M- QbPb}{Pa}$

$Qa = \frac {M}{Pa} - \frac {QbPb}{Pa}$ This is the equation of the budget line.

Qa =$\frac {90}{3} - \frac {QbPb}{Pa}$

$Qa = 30 - \frac {3Qb}{3}$

Assuming the 1:1 ratio of usage, 15 units of A and 15 units of B will be bought at the price of 3 birr

$15 = 30 - Qb$

$Qb = 15\space units$

$Qa= 15\space unit$

ii)

When the price is increased to 6 birr while maintaining the 1:1 usage of two commodities

1 commodity of A = 6 birr

1 commodity of B = 3 birr

One usage costs= 9

To find the consumed pair of commodities, we compute $\frac{90}{9}= 10$

Therefore the quantities are;

$Qb = 10 \space units$

$Qa = 10 \space units$units

III)

The kind of preference is the perfect complements.

This type of preference has the right angle indifference curve as shown below.