1. Consider a Cobb-Douglas utiltiy function of the form U (x,y,z) = xyz with three consumer goods, x, y and z:

Set up the Lagrangian maximization problem

Solve for the Marshallian Demand for goods x, y and z respectively

Compute the income effect for good x

Compute the the cross price effect of a price change for good x on consumption of good y

Solve for the indirect utility function

Solve for the optimized Lagrange multiplier, Lambda* , and show that it is equal to the marginal utility of income

2. An economic bad is something you don't want to consume, i.e. less bad is better. Define an economic bad mathematically and name one economic bad in reality. Suppose you had to consume a certain amount of a given economic bad but could pay to get rid of it. What would the Marshallian Demand curve for the economic look like? Draw it in the Price-Quantity axis (hint: be careful to defne the price of economic bad here!).