Suppose the utility function for goods x and y is given by utility = U(x,y)=xy+y

Question

Suppose the utility function for goods x and y is given by
utility = U(x,y)=xy+y

a. Calculate the uncompensated (Marshallian) demand functions for x and y and describe how the demand curves for x and y are shifted by changes in I or the price of the other good.

b. Calculate the expenditure function for x and y.

c. Use the expenditure function calculated in part (b) to compute the compensated demand functions for goods x and y. Describe how the compensated demand curves for x and y are shifted by changes in income or by changes in the price of the other good.

Explanation / Answer

to solve for demand function put MRS= px/py i.e. y/ (1+x) = px/py now use px * x + py *y= m { eliminate y to calculate demand fn of x} u will get px= m/(2x +1) similarly, to calculate demand function for y py= (m+ px )/ 2y

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