Cero has utility U = -{(x -50)^2+ (y -40)^2}, Px = Py = 1 and M = 100. a.If he r

Question

Cero has utility U = -{(x -50)^2+ (y -40)^2}, Px = Py = 1 and M = 100.

a.If he receives an additional 10 income how does he spend it? Just on x, just on y or some on x and some on y or on neither? Ted has utility U = 5x^2+ 8y^3 Px = 1 Py = 2 a.At what income is Ted indifferent between buying only x or only y?

b.If income were above the level found in part a, which good would he buy exclusively?

c.If income were below the level found in part a, which good would he buy exclusively?

d.Would the same answers for parts a, b, c hold true if utility were U = 10x^2+ 16y^3and why or why not?

Josh has utility U= -min{4x, 5y} Px=7 Py=10 M=140

a.What is the highest utility he can get?

b.What is his optimal point?

Explanation / Answer

Cero's Case :-  U = -{ (x-50)2 + (y-40)2 } Where Price of Good x = 1 and Price of Good y=1 and Income=M=100

a). If he receives an additional income of 10

In the given case the utility function is negative, this means that cero obtains negative satisfaction from consumption of goods x and y. Thus whether he spends his additional income completely on good x or completely on good y or a combination of both the goods , all will result in a negative utility.

In this case the total utility or the total satisfation obtained by cero after consumption of goods x and y is negative . hence the marginal utility or the addtional utility derived by cero by consuming an additional unit of goodx or y or both is negative.

If he consumes any good , his utility will further decrease.

Hence he will NOT consume any good.

Ted's case:- U=5x2 + 8y3 where Px=1 and Py=2

a.) Let M be the income at which Ted is indifferent in buying only x or only y.

If he buys only good x then, U=5x2 total utility derived. Similarly if he buys only good y then, U=8y3 is the total utility derived. and since he is indifferent between good x and y at this level, hence 5x2=8y3 (equation 1 )

Px * Qx + Py * Qy = M ( budget line equation)

If he buys only x then, 1*x + 2*0 = M   

or, x=M

Similarly if he buys only good y

or, y=M/2

Now substitute values of x and y in equation 1,

5*M2 = 8*(M/2)3 or, 5/8 M2 = M3/8

or, 5/8 = M/8 or, M=5 Hence income at which ted is indifferent in x and y if he buys either of the two completely is 5

b) If the income is above 5 in case a then ted would buy more of that good which gives him highest level of satisfaction at that level of income.

Hence he would buy more of such good at a higher income to gain more total utility.

c) If the income is less than 5 in case a then ted that good exclusively which gives him most higher level of satisfaction at that level of income.

d.) Yes the answer would remain same as the utility is only multiplied by 2 here. U' = 10x2+16y3

or,U'= 2*( 5x2+8y3)

or, U'=2U In this case utility is only multiplied by 2 hence no effect on choices made.

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