A consumer has preferences for two goods, x, and y, expressed by the following utility function:

U(x,y)=x^1/3*y^2/3

The price of x is PxPx, the price of y is PyPy and her budget is $1500. The consumer wishes to choose the quantities x and y that maximize her utility subject to her budget constraint.

1. Write down the consumer's budget constraint.
2. Write down the Lagrangian for this constraint optimization problem.
3. Using the principles of constraint optimization, find out the optimal demand function for both goods xx and yy.
4. Find the price elasticity of demand for good xx at the equilibrium and interpret the meaning of the elasticity.