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(a) Derive the Marshalian demand functions and the indirect utility function for the following utility function:
u(x1, x2, x3) = x1 1/6 x2 1/6 x3 1/6 x1≥ 0, x2≥0,x3≥ 0
[Hint: Try to make use of your results from problem 3 in Assignment 1 instead of redoing all the calculations here.]
(b) Using the indirect utility function that you obtained in part (a), derive the expenditure function and from it, derive the Hicksian demand function for good 1.
(c) Jack and his grandfather are sitting at the dinner table, discussing their lives. Both share the same utility function as given in part (a). Jack is boasting about his $5000 a month salary, with per-unit prices of x1, x2 and x3 being $4, $4 and $16 respectively. Jack's grandfather claims that the old days were much better because although his salary was $500 a month, the per-unit prices of x1, x2and x3 were all only $1. Do you agree with his grandfather?
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
Each week Jaime saves $25. How long will it take her to save $350? Divide $350 by $25; 350 ÷ 25 = 14 weeks.
triangle
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