Consider the utility function u1(x1,x2)=V xq + x2 (a) Calculate the MRS. Is the preference homothetic? Explain. (b) Does

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Consider The Utility Function U1 X1 X2 V Xq X2 A Calculate The Mrs Is The Preference Homothetic Explain B Does 1 (135.77 KiB) Viewed 44 times

Consider the utility function u1(x1,x2)=V xq + x2 (a) Calculate the MRS. Is the preference homothetic? Explain. (b) Does the utility function u2(x1,x2)=51n(/xq +x2 = 2000 represent the same preference as uz? If yes, show mathematically that given any two bundles A = =(xa 24,x) and B = (x®, x® 2), if A is preferred to B under uq, = then A must also be preferred to B under U2 = If no, find a pair of consumption bundles that contradicts the claim. In other words, find two consumption bundles A = (x^,,x92) and B = (x® 7,x) such that A is preferred to B under uy, but Bis preferred to A under u2. (You need to provide actual numbers for the two bundles.) 1 (c) Repeat (b), but this time compare u, with the utility function uz(x1,x2) = √x + √x2 (d) Repeat (b), but this time compare u, with the utility function 44(X1,x2) = xy + x2. ។