I understand how to get them but when it comes to computing I always lose my way.

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 Mark'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.
12. Using the Indirect Utility Function obtained in 7, derive the expenditure functione(p₁, p₂, U).
13. Usingtheexpenditurefunctione(p₁, p₂, U), derive the Hicksian Demand Functions for good 1 and good 2 using Shephard's Lemma.
14. Verifythatthevalueoftheexpenditurefunctione(p₁, p₂, U)isequal to zero whenUtakes on the lowest level of utility.
15. Demonstratethattheexpenditurefunctionishomogenousofdegree one in prices.
16. Demonstratethattheexpenditurefunctione(p₁, p₂, U)isstrictlyin- creasing inU.
17. Demonstratethattheexpenditurefunctione(p₁, p₂, U)isstrictlyin- creasing inp₁.
18. How much of good 1 will Mark buy?
19. Calculate the uncompensated own-price elasticity of demand for good 1. Is the demand for good 1 price elastic, inelastic or unit elastic?
20. Calculate the income elasticity of demand for good 1. Is good 1 normal or inferior? Why? If good 1 is normal, is it a luxury good or a necessity good? Why?
21. Calculate the compensated own-price elasticity of demand for good 1. Interpret this result. Compare this to your answer in part 19 and explain the difference.
22. Demonstrate that the Marshallian Demand Functions satisfy Cournot Aggregation.
23. Demonstrate that the Marshallian Demand Functions satisfy Engel Aggregation. Suppose the price of good 1 increases by $5.
24. Given this price increase, calculate the Total Effect, Substitution Effect and Income Effect using the (Discrete) Slutsky equation.
25. Calculate the compensating variation for the increase in p₁.
26. Calculate the equivalent variation for the increase in p₁.
27. Find the equation of the Marshallian demand curve for good 1 given that the price of good 2 is $10 and his income is $200. Based on this equation, calculate the change in his Marshallian consumer surplus due to the increase in p₁.