Suppose that income is M, and prices are P1 and P2, and consider the following utility function:

a. Using Lagrangian, derive the ordinary demand functions of and .

b. Suppose M=$100, and prices are P1=$20 and P2=$20; calculate the utility maximizing quantities of and . If price of good 1 drops to $10, what would be the demand for . Using this infomation, draw a demand curve of .

for a, do I just need to find the partial derivative of U with respect to , and , then divide by ?

and I need some hints on b