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.
(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"
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