Question

2. Jane's utility function has the following form: U (1,y) = 3x2 +2.ry The prices of cand y are p, and Py respectively. Jane's income is I. (a) Find the Marshallian demands for and y and the indirect utility function. (b) Without solving the cost minimization problem, recover the Hicksian de mands for x and y and the expenditure function from the Marshallian demands and the indirect utility function. (c) Write down the Slutsky equation determining the effect of a change in P, on the demand of x. Indicate which component represents the total price effect, which component represents the substitution effect, and which component represents the income effect. (d) Now assume that pe = 64, Py = 2, and I = 100. Using the Slutsky equation from part (c) compute the total, substitution, and income effect of a change in P, on the demand of x.

Answer 1

Solution: UCy3x+2xy mays halls damand tor x andy and indreat ufily fnetn at eauilibrimn: mux Py 6py 1PyP 2yPyCA-6Pyu Budget Canstraint PMtPy 3x Pr-6xfy 2I 2-I 7 3 (A-2Py)

2 and Ar-6 f-ry) 2 Py -Gy) PyJ L3)(P) I (3fx- 6 The Hicksian damand for and y ares The inverse oti)-tymetion is: 3 (22) 2 3 PA-6Py 2. CPx-6Ry 2- Py (3 f-Gty

1a Py 4-(-6) V :2ty Py C3P-Gey) eyfi) C-Gy) 2 HLA-3Py 2- -3Py) and E P-3P) U Py 3 CA-6) PA-3 Py

Qnd E CSlotiky ewatm is The sloteky eauatim i9ien o, i3 pmce effect tota). &u Btitutian cfect G1 income epfect Iloo Gan P Gy, Py 2 1 2 and vale in Bobrtitutng hen tho?e value