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Anne has specified 9500 SEK as the monthly budget for consumption of two goods (called A and B). The prices of the goods are pA-500 and pB = 2000, respectively. Use the rational spending rule and the budget constraint to calculate the quantities she should consume to maximize her utility, UAQB QAQB? What is her maximum utility?
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Answer #1

Answer:

Given

Budget B=9500

PA=500

PB=2000

so budget line is

PA*QA+PB*QB=B

500*QA+2000*QB=9500 Eq 1

U=QA+QB+QA*QB

Marginal Utility for QA MUQA=dU/dQA=1+QB

Marginal Utility for QB MUQB=dU/dQB=1+QA

For Utility Maximisation

MUQA/MUQB= PA/PB

(1+QB)/(1+QA)=500/2000

QA=3+4QB Eq 2

From equation 1 and 2

500*(3+4QB)+2000QB=9500

QB=2 units

QA=3+4*2=11 units

Maximum Utility U=11+2+2*11=35 units

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