just do part c and explain it 1.This question will let you examine/explore a more interesting utility func-tion than the simple example discussed in class as there will be both cross-price elas-ticity and an inferior good. Suppose you are told a consumer has the following utilityfunction:U (9219₂) = 9z+√9z+ 9₂You should assume income is Y, the price of good r is P2, and the price of good z isP₂. This question will ask about several concepts discussed in lecture.(a)What is the Marshallian demand for goods x and z? I.e. find (qq)for both interior solutions and corner solutions. Note: the outcome is "ugly"for the interior section and both corner should include constraints, i.e. limitsusing Y relative to f(P, P₂). Hint: if solving using MRS = MRT, can use thisinformation again in part (d).(b)Suppose you are told P₂ = $8 and P₂ = $1. Create a graph showing theIncome Consumption Curve (ICC) for Y = {$12.25, $35, $49, $70, $98). Be sureto clearly label the graph. Based on the ICC, which of the goods is the inferiorgood? Note: this should help with the corner solutions found in part (a), i.e. youshould be able to check the "criteria," i.e. Y vs f(P, P₂).(c)Graph the Engel curve for good z from Y = $0 to Y = $100 givenP₁ = $8 and P₂ = $1. Hint: there should be 3 parts as the demand function has3 parts with the changes to the Engel curve consistent with the outcome in part(b).(d)Find the Hicksian Demand for the interior solutions as a function ofPr, P₂, and Ū, i.e. find (qq). What is the Expenditure function E(P, P₂, Ū)?Hint: you can use MRS = MRT you found in part (a) and solve for q₂ =f(qz, PT, P₂) as this will make finding a solution much easier.(e)Using from part (a) and q from part (d) with P₂ = $8, P₂ = $1,and Y = $70 find what the Substitution Effect and Income Effect from a +$0.05change in the price of good z. Does your answer make sense? Explain why orwhy not. Note: values for q with P₂ = {$0.95, $1.05} are not "nice" values andyou should include 4 decimal places when giving the answer.(f)Suppose the consumer's income remains Y = $70, but the price of goodx increases to P₁ = $18 and the price of good z increases to P₂ = $2. What isthe Compensating Variation? What is the Equivalent Variation? Note: givenyou found the Expenditure function in part (d), this should be relatively straightforward.

The Engel Curve is the graphical presentation of effect of changes in income on demand for goods. In…

1. This question will let you examine/explore a more interesting utility func- tion than the simple example discussed in class as there will be both cross-price elas- ticity and an inferior good. Suppose you are told a consumer has the following utility function: You should assume income is Y, the price of good x is P2, and the price of good z is P. This question will ask about several concepts discussed in lecture. (a) (b) (c) What is the Marshallian demand for goods x and z? I.e. find (9) for both interior solutions and corner solutions. Note: the outcome is "ugly" for the interior section and both corner should include constraints, i.e. limits using Y relative to f(P, P.). Hint: if solving using MRS = MRT, can use this information again in part (d). Suppose you are told P₂ = $8 and P₂ = $1. Create a graph showing the Income Consumption Curve (ICC) for Y = {$12.25, $35, $49, $70, $98}. Be sure to clearly label the graph. Based on the ICC, which of the goods is the inferior good? Note: this should help with the corner solutions found in part (a), i.e. you should be able to check the "criteria," i.e. Y vs f(P₂, P₂). Graph the Engel curve for good z from Y = $0 to Y = $100 given P₁ = $8 and P = $1. Hint: there should be 3 parts as the demand function has 3 parts with the changes to the Engel curve consistent with the outcome in part (b). (d) P₁, P., and Ū, i.e. find (q). What is the Expenditure function E(P₂, P.,Ū)? Hint: you can use MRS = MRT you found in part (a) and solve for q = f(qz, Pz, P.) as this will make finding a solution much easier. Find the Hicksian Demand for the interior solutions as a function of (e) (f) Using q from part (a) and q from part (d) with P₂ = $8, P₂ = $1, and Y = $70 find what the Substitution Effect and Income Effect from a +$0.05 change in the price of good z. Does your answer make sense? Explain why or why not. Note: values for q with P₂ = {$0.95, $1.05} are not "nice" values and you should include 4 decimal places when giving the answer. Suppose the consumer's income remains Y = $70, but the price of good x increases to P₂ = $18 and the price of good z increases to P = $2. What is the Compensating Variation? What is the Equivalent Variation? Note: given you found the Expenditure function in part (d), this should be relatively straight forward.