Question

Exercise 6. Bottled Water (Quasilinear) Water is an essential good, but brand bottled water has substitutes (other brand bottled water). Your utility from drinking the brand SmartWater is u = x1 + x2, where xi is the number of SmartWater bottles you consume in a day, and x2 is consumption of everything else you purchase in a day. a) What is the marginal utility (MU1) of consuming an extra bottle of SmartWater? Does the utility you get from an extra bottle diminishes the more you drink? b) What is the marginal utility (MU2) of consuming an extra unit of everything else (x2)? Do you have increasing/decreasing/constant marginal utility for consumption of x2? c) What is the marginal rate of substitution, MRS, between SmartWater (x1) and all other consumption goods (x2)? d) You and your friend have the same identical utility function, and you both drink 4 bottles of SmartWater a day. However, you consume 10 units of everything else, while she consumes 20 units of everything else. How does your utility differ? How does your MRS differ at those two different consumption bundles?

Answer 1

Enercise 6 He the utility function is U= x/2 +22 where X is the numbu of smart wath bottles and X2 is the consmption of everything else. marginal utility of consuring an entra bottle of Smart wath -MUL--% 2X1 now.. d (mui) - 16-)x=272 dxi - -- ** - 3/2 20 | Here as d (mui) to this means that the utility dk Iwe get from an entra bottle diminishes the more wedrink b consuring an enta mait of Marginal utility (MU2) of Jevrything else (XL) is Muze ou - 282 dX2 and d (MU2) = 0 Hue, as d (MU2)=0 then we have constant marginal X2 I utility for consumption of X₂ o Now the marginal rate of substitution MRs between Smart wath (x1) and all other consumption goods (14 I will be danned with Hanscanner

MRS .MUL MUZ or the absolute value of MRS MRSL- MUI - II MUL = £ x, 1/2 - 1 x,-12 d I and my friend have Tie. U= x ² + x2 the same utility faction Now, I consime 4 bottles of smatwath and 10 mit of evaything else, hence by substituting X1 =4 and X2 = 10, the utility will be Us (4) + 10 = 12 utils and my friend consumes 4 bottles of smont with and o 20 nits of evny thing else. Hence by substituting x1 = 4, X 2 = 90 the utility will be U= (4) % + 20 = 22 utils | Hunce my fricud's utility is (22-12) or lo util. higher than my utility. Now, when 8, = 4, X2 =10 then (MRS/ - / x - ² = 1 (4) -12 -0.25 and when X 1 = 4 X2 = 20, then / MRS) = ² x 1-² - Ž 147-22 - 0.25 Hince MRS remains same for both of us for thes two consumption en bundles cs