Your utility function is U=10X0.1Y0.7 and your marginal utility functions are

Mux=X-0.9Y0.7 and MUy=7X0.1Y-0.3

Your budget is M and the prices of the two goods are Px and Py.

a) Write down the two conditions for utility maximization subject to a budget constraint.

b) Derive the demand functions for X and Y.

c) Based on your demand functions explain whether:

1. Y is a normal good or an inferior good and why.
2. good X satisfies the law of demand.