5. For each of the following assertions, first state whether it is true or false. Then, provide full support for your statement by using theorems, definitions and/or examples where applicable. No...

Only from c onwards


Extracted text: 5. For each of the following assertions, first state whether it is true or false. Then, provide full support for your statement by using theorems, definitions and/or examples where applicable. No marks will be awarded for unsupported statements. (a) Consider the utility function U(x1, x2) = (x + x%). The marginal rate of substitution of good x2 for good xi is equal to (b) Let u(x) represent some consumer's monotonic preferences for æ e R. If f(x) = u(x) – 10 000, then f (x) also represents these preferences. (c) A consumer's preferences are defined over R? as (x1, x2) ► (y1, Y2), if x1 + x2 < y1="" +="" y2:="" these="" preferences="" are="" both="" locally="" non-satiated="" and="" strictly="" monotonic.="" (d)="" the="" preferences="" of="" a="" consumer="" with="" utility="" function="" u="" (x1,="" x2)="(1+x1)(1+x2)" are="" convex.="" [note:="" you="" may="" assume="" that="" consumption="" is="" confined="" to="" the="" non-negative="" quadrant="" of="" r2,="" i.e.="" x1="" 20="" and="" x2=""> 0). (e) The degree of homogeneity in prices of the Marshallian demand function r,(p, y) a+3 pi implies that there is no change in the demand for good i as prices increase.