Bundle: Microeconomic Theory: Basic Principles and Extensions, 12th + MindTap Economics, 1 term (6 months) Printed Access Card
Bundle: Microeconomic Theory: Basic Principles and Extensions, 12th + MindTap Economics, 1 term (6 months) Printed Access Card
12th Edition
ISBN: 9781337198202
Author: NICHOLSON, Walter, Snyder, Christopher M.
Publisher: Cengage Learning
Question
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Chapter 4, Problem 4.1P

a)

To determine

To find: Quantity of Twinkies and soda that maximizes utility.

a)

Expert Solution
Check Mark

Explanation of Solution

Given utility, U = tsBudget constraint, tPt+sPs=IMRS=MUtMUsU=tsMUt=dUdtMUt=12(st)1/2MUs=dUdsMUs=12(st)1/2

Budget constraint:tPt+ sPs = IMRS = PtPsMUtMUs=PtPs12(st)1/212(ts)1/2=PtPs(st)1/2(st)1/2=PtPsst=PtPss=t.PtPs..........(1)Insert (1) budget constraint.tPt(t.PtPs)Ps = It = I2PtSo,s = t.(PtPs)s=I2Pt.PtPsPlug Pt= 0.10, Ps= 0.25, I = 1t=I2Pt=12(0.10)=5s=I2Ps=12(0.25)=2

Therefore, to maximize utility there should be 5 Twinkie and 2 soda.

b)

To determine

To find: The calculation of new allowance.

b)

Expert Solution
Check Mark

Explanation of Solution

U = tsU = 5×2U = 10

After inserting the t and s function in the budget constraint:

U=I2Pt.I2PsU=I2Pt.PsPlug U = 10,Pt=0.40,Ps=0.25U=I2Pt.Ps10=I2(0.40)(0.25)Solve for the I,I = 2

The allowance should increase from $ 1 to $2.

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