1. An individual consumer's utility function and the budget constraint are described below.(ch. 5).U = xys.t. m = Pxx+Pyywhere, m = $100, Pz = $5, and py = $2.Note: 2 and y are the amount of x good and y good; m the amount of money, på theprice of x good; Py the price of y good.(i) Find the marginal rate of substitution between x and y.(ii) Find the slope of the budget constraint (in value). [no need to draw the budgetconstraint.](iii) Given the answers to (i) and (ii), find the optimal amount of each good, x* and y*.(iv) Find the level of utility obtained by this rational consumer.(v) Interpret the meaning of the answer you found in (iii) and (iv).

Optimal choice occurs when Marginal rate of substitution= slope of budget constraintUtility is given as U=xy Marginal utility of x & y are respectively MUx=∂U∂x=yMUy=∂U∂y=x Marginal rate of substitution, MRS MRS=-MUxMUyMUx=yMUy=xMRS=-yxii) Budget constraint is given as m=xpx+ypyypy=-xpx+my=-xpxpy+mpy Which is equivalent to general equation of strainght line y=mx+c, where m is the slope Comparing budget constraint with general equation we get slope=-pxpy px=$5py=$2Slope=-52 iii) For optimal consumption MRS=slope of budget constraint MRS=-yxslope=-52-yx=-525x=2y Put the above condition in budget constraint we get m=xpx+ypym=$100,px=$5, py=$2100=5x+2y5x=2y100=5x+5x10x=100x*=105x=2y5*10=2yy*=25 Hence, optimal consumption of good x=10 units & good y=25 units iv) Utility,U=xy x=10,y=25 U=10*25 U=250iii) With given budget consttraint, consumer should consume 10 units of good x and 25 units of good y to maximize her utility iv) With given budget constraint, the consumer can achieve a maximum of 250 units of satisfaction from her optimal economic decisions

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1. An individual consumer's utility function and the budget constraint are described below. (ch. 5). U = xy s.t. m = pr+Pyy where, m = $100, pr = $5, and py= $2. Note: r and y are the amount of x good and y good; m the amount of money, pz the price of x good; Py the price of y good. (i) Find the marginal rate of substitution between 2 and y. (ii) Find the slope of the budget constraint (in value). [no need to draw the budget constraint.] (iii) Given the answers to (i) and (ii), find the optimal amount of each good, x* and y*. (iv) Find the level of utility obtained by this rational consumer. (v) Interpret the meaning of the answer you found in (iii) and (iv).

1. An individual consumer's utility function and the budget constraint are described below. (ch. 5). U = xy s.t. m = pr+Pyy where, m = $100, pr = $5, and py= $2. Note: r and y are the amount of x good and y good; m the amount of money, pz the price of x good; Py the price of y good. (i) Find the marginal rate of substitution between 2 and y. (ii) Find the slope of the budget constraint (in value). [no need to draw the budget constraint.] (iii) Given the answers to (i) and (ii), find the optimal amount of each good, x* and y*. (iv) Find the level of utility obtained by this rational consumer. (v) Interpret the meaning of the answer you found in (iii) and (iv).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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part C D
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