I solved questions a b c. I just need help with d e f g. Thank you

Exercise 7.2 One of the exercises in Chapter 5 required that we solve the following [UMP] : 1-0 mm: 1:" I.\" y 3-t- P33: + pyy = m to obtain the Lagrange multiplier, X', Marshallian demand functions mm (p3. py, m.) and ym (pr, pg, 117.). and the indirect utility function v (30,, p1,, in). Another exercise, this time in Chapter 6', required that we solve the corresponding [EM P] : $1.151 pan: + Full s.t. :\"y1"' = U to obtain the Lagrange multiplier 17', Hicksian demand functions an. (19,, Py, U) and y}, (p3. pg, U ) , and the expenditure function e [pnpw U). Using the results from these two exercises verify the following statements. a. Recall that m is a parameter. which means we can set its value to any number we want. Show that if we let m = e (ngpy. U), then Matshallian demands are equal to Hicksian demands. b. Recall that U is a parameter, which means we can set its value to any number we want. Show that if we let U = 0 (pg. pwm), then Hicksian demands are equal to Marshallian demands. c. Explain graphically, making sure that you label everything clearly, what is going on. Use a plot of the budget constraint and the indifference curve of the consumer. Be sure your explanation includes justication for the equivalence of the two problems and, in particular, for parts a. and b. CL Show that if we let m a e (pr, 33,, U) then the indirect utility function evaluated at this value is equal to the target utility level, U, of the [EM P] : \"(pl'plllm = e(p1vpyvU)) = U. Can you show that this implies that the expenditure function and the indirect utility functions are inverses of each other? e. Show that if we let U a- v (pmpm m) then the expenditure function evaluated at this value is equal to the consumer's income in the [UMP] , m : 3(1'11 me a \"(Phi-W. 111)) I m. Can you Show that this implies that the expenditure function and the indirect utility functions are inverses of each other? 1'. Explain your results intuitively and graphically. 3. Show that x = i. q and explain the intuition of your result