Question

A consumer has an income of $120 to buy two goods (X, Y). the price of...

A consumer has an income of $120 to buy two goods (X, Y). the price of X is $2 and the price of Y is $4. The consumer utility function is given by ?(?, ?) = ? 2/3 ∗ ? 1/3 You are also told that his marginal utilities are ??? = 2 3 ( ? ? ) 1/3 ??? = 1 3 ( ? ? ) 2/3

1. Find the slope of the budget constrain. (1 point)

2. Calculate the optimal quantity of good X and Y for this consumer (Point A). (2 points)

Assume that the price of good X increases to ?? ′ = $8, and holding everything else constant:

3. Graph all your findings by showing the change in price if good X along the points A and B. (2 points)

Hint: Do not compute and graph point C. Research studies found the demand for good X as follow: ? = 8 −0.4 ∗ ?? + 0.2 ∗ ?? +0.05 ∗ ? where, ?? is the price of good X, ?? is the price of good Y, and M is consumer’s income.

4. Based on this research finding and holding everything else constant, can the consumer afford to buy 12 units of good X. Explain. (2 points)

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