Question

2. Janice consumes two goods, X and Y. Janice has a utility function given by the expression: U = 4x0.5y 0.5 The current prices of X and Y are $25 and $50, respectively. Janice currently has an income of $750 per time period (Put X on the horizontal axis and Y on the vertical axis). a) Is the assumption that "more is better” satisfied for both goods? b) Calculate MRSxy. Determine if it is diminishing for this utility function. c) Express the budget equation mathematically. d) Draw a graph to illustrate the shape of a typical indifference curve. Label the curve U). Does the indifference curve intersect either axis? On the same graph, draw a second indifference curve U2, with U2>U.

Answer 1

27 U = 4x05 yous a) Yes, "More is better " is satisfied for both goods. 1. Let's see ff 'x' is Smureased by a factor la suhere asi do, Vas 4 (ax)0% y05 As, a> . Va> u - Hence with higher 'X' we get higher ritility Similarly for y by a factor 'b' where b> i ao, Us = 4 40.5 (by) 0:5 2 U = busu Ab, byl So, U>

Hence with higher '4' me get highes utility, &o, "More is better" for both goods b) MRS xy = du/dx m du/dy MRS : d 4xos yo.5 / d 4x05 yo.5 1 dx I dy ) 25 X0.5 = - 2 :- 270.5 70.5 - 2X0.5 X 5 y Fax disinishing Mrs MORI 2 MRSXY So, pa sve dy <0. o δY

So, MRSA, is diminishing . a) Budget regnation :- Pedt Pyry SM Where, Pax - Priced " A ly price of y' As, Pa = 25 ; Py = 5o & M = 750 (briven) Son [ 25a + soy $ 750 t is the budget Equation 19 Incomie : - Uz - cu a curne does not intersect either No, Indifferenced curne does not interne for u(219) = 4Xo's you wais