Supposed Mark exclusively derives utility from the consumption of two goods, namely x₁ and x₂ with prices p₁ and p₂ respectively. His utility function is given as U(x₁,x₂)=(x₁^0.5+x₂^0.5)². The domain of the function is that x₁, x₂, p₁, p₂ > 0.

1. Calculate the marginal utility derived from consuming x₁and x₂. Do these marginal utilities support the assumption of non-satiation?
2. Does Justin's consumption preference also indicate that his preferences obey the Law of Diminishing Marginal Utility?Show your solution.
3. Obtain the marginal rate of substitution for good 1 and good 2(MRS₁₂).
4. Solve for the values of the Marshallian Demand Functions for good 1 and good 2.
5. Demonstrate that the Marshallian Demand Functions are homogenous of degree zero in prices and income.
6. DemonstratethattheMarshallianDemandFunctionssatisfyWalras' Law.
7. Obtain Mark's Indirect Utility FunctionV(p₁, p₁, m).
8. Demonstrate that the Indirect Utility Function is homogenous of degree zero in prices and income.
9. Demonstrate that the Indirect Utility Function is strictly increasing inm.
10. Demonstrate that the Indirect Utility Function is strictly decreasing inp₁.
11. Demonstrate that the Indirect Utility Function satisfies Roy's Identity for good 1.