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