PROBLEM 3 – Slutsky Equation, Income Effect, Substitution Effect, and Total Effect There are two goods which quantities are to be denoted by x and y, while prices are denoted by px and py, respectively. There is a consumer whose income is to be denoted by I and utility by u. His expenditure function is known to be: *see image* Suppose the consumer already spend $90 on good x which cost $1 and good y which cost $1, and initially purchase 60 of good x and 30 of good y. i. If the price of good x increase to $2, how many will he purchase each of the goods? ii. How much of the decrease in his demand for good x is due to the fact that they have become relatively more expensive? How much is due to the fact that his overall purchasing power has decreased? [Hint: find first the initial utility before the price change and income level needed to reach those initial utility with new prices. Slope of the indifference curve is given by MRS = -2y/x] iii. Based on your answer, draw it in a graph indicate the direction of each effect and derive the compensated and uncompensated demand curve for good x. Are they different or same? Which one is steeper? Why?
PROBLEM 3 – Slutsky Equation, Income Effect, Substitution Effect, and Total Effect
There are two goods which quantities are to be denoted by x and y, while prices are denoted by px and py, respectively. There is a consumer whose income is to be denoted by I and utility by u. His expenditure function is known to be: *see image*
Suppose the consumer already spend $90 on good x which cost $1 and good y which cost $1, and initially purchase 60 of good x and 30 of good y.
i. If the
ii. How much of the decrease in his demand for good x is due to the fact that they have become relatively more expensive? How much is due to the fact that his overall
iii. Based on your answer, draw it in a graph indicate the direction of each effect and derive the compensated and uncompensated demand curve for good x. Are they different or same? Which one is steeper? Why?
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