Question

A consumer has a demand function for rice of the form:

X = 3 + m/2p

Assume that his/her income per month that is allocated to consumption of rice in a month is kshs 600/-The price of one kg of rice is kshs 100/-. During harvesting, the price of rice falls by shs 25 per kg.

Compute the consumption of rice by the consumer in a month before and after the fall in price.

Compute the Substitution Effect on the consumer

Compute the Income Effect

What is the total effect of the price change?

A consumer is faced with the Utility function of the form:

U(x,y) = αLogx + βLogy

If this Utility function is represented by a map of indifference curves, find the slope of a particular indifference curve at any point.

Answer 1

(a)

Consumption before:

$x=3+\frac{m}{2p}$

$=3+\frac{600}{2\times 100}=6$

Consumption after:

$x=3+\frac{m}{2p}$

$=3+\frac{600}{2\times75}=7$

(b)

Substitution Effect:

$=x_h-x_0$

$=3+\frac{600\times (\frac{75}{100})}{2\times 75}=3$

(c)

Income Effect:

$=x_1-x_h$

$=3+\frac{600}{2\times75}-3+\frac{(600\times\frac{75}{100})}{2\times 75}=1$

(d)

Total Effect:

$=3+\frac{600}{(2\times100)}-3+\frac{600}{(2\times75)}=-1$