Jack derives utility from Hokey course (H) and Chess course (C) as given by the following utility function: U (H, C) = √HC The average price for the hokey course is 20 dollars and for chess course16 dollars. Moreover, Jack has a budget of 80 dollars. a) Use Lagrange optimization method to find Jack’s utility maximization choice of consumption bundle. Find also his utility level from consuming that bundle. b) Assume that price of chess course increases to 25 dollars. Suppose Jack also changed his budget for consumption and we do not know it. Denote Jack’s budget by α and find his demand for H and C under the new conditions as a function of α. c) Find the income level which is necessary to make Jack reach the same utility level as before the price change.
Jack derives utility from Hokey course (H) and Chess course (C) as given by the following utility function:
U (H, C) = √HC
The average
of 80 dollars.
a) Use Lagrange optimization method to find Jack’s utility maximization choice of consumption
bundle. Find also his utility level from consuming that bundle.
b) Assume that price of chess course increases to 25 dollars. Suppose Jack also changed his budget for
consumption and we do not know it. Denote Jack’s budget by α and find his
under the new conditions as a function of α.
c) Find the income level which is necessary to make Jack reach the same utility level as before the
price change.
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