s$)2.$ A person consumes two goods x and y$.$ Let px and py be the prices of these two goods and assume that py $=1.$ The person$$s indirect utility function is $,$ where a and b are positive constants.

a$)$ Derive the Marshallian demand function for x$,$ using Roy$$s identity. $(2$ points$)$

b$)$ Find the direct utility function. $(8$ points$)$

c$)$ Derive the Marshallian demand by maximizing the direct utility function. Is the result consistent with what you found in a$)?(6$ points