Question

Andy purchases only two​ goods, apples​ (a) and kumquats​ (k). He has an income of $200 and can buy apples at ​$22 per pound and kumquats at ​$11 per pound. His utility function is:

​U(a,k)equals=5a+3k.

That​ is, his constant marginal utility for apples is 55 and his constant marginal utility for kumquats is 33.

What bundle of apples and kumquats should Andy purchase to maximize his​ utility? ​ Why?

Andy should maximize his utility buy purchasing ____ apples​ (lbs.) and ____ kumquats​ (lbs.).  ​(Enter your responses rounded to the nearest whole​ number.)

Answer 1

Budget Line Equation:

PxQx + PyQy = I

22Qx+ 11Qy = 200 where I is income

Px = Price of apple, Py= Price of kumquats

Since utility function is of perfect substitute.

Therefore utility maximization there will be any one of the three cases follows:

Case1: MRS > Px/Py

Case2: MRS < Px/Py

Case3: MRS = Px/Py

MRS is the slope of the indifference curve and Px/Py is the alope of the budget line.

MRS = MUx/MUy

= 5/3

Slope of Budget Line = Px/Py

= 2

Since MRS< Px/Py

It means consumer will spent all his money on kumquats as they are cheaper than apple. He will consume all his income by consuming kumquats.

Optimal Bundle is = (0, M/Py)

= (0, 200/11)

= ( 0, 18)

where 0 is quantity of apples

and 18 is the quantity of kumquats.

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