U(x1,x2)=x1 +x2^(0.5)

a)Find the consumer's Marshallian demand functions for both goods using lagrangian. What are the price and income elasticities for these two goods (own price, cross price, and income). Explain your results.

b)Using the demands found in a) solve for the consumer's indirect utility function. Using this function find the consumer's marginal utility of income. Verify Roy's identity for both goods. Show that indirect utility is increasing in income and homogenous of degree zero in prices and income, and explain why it is so.

c)Formulate and solve the expenditure minimization problem for this consumer to find their Hicksian demand functions. What are the elasticities of the Hicksian de- mands with respect to own and cross prices? Are these elasticities different from what you found in a), if so, why are they different? What restriction on income and prices are needed in order for the consumer to have an interior solution to their optimization problem?

e) Find the consumer's expenditure function. Then verify the Slutsky equation for good one and translate it into a relationship involving elasticities. Link your result to those you found in a) and c).