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Suppose the Utility function of the consumer is given by U = x + 5y^3 Suppose...

Suppose the Utility function of the consumer is given by

U = x + 5y^3

Suppose the price of x is given by p x and the price of y is given by p y and the budget income of the consumer is given by I. Price of x, Price of y and Income are always strictly positive. Assume interior solution.

a) Write the statement of the problem

b) Compute the parametric expressions of the equilibrium quantity of x & y purchased and the maximized utility. You can either use Lagrangian or the alternative to Lagrangian (i.e. tangency and the budget constraint).

c) Compute the slope of the marshallian demand curve for x. Is it always downward sloping? Why or Why not?

d) Is x a normal or an inferior good? How will you formally (i.e. mathematically) prove it?

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