Perfect Complements: 3 Goods Case 3. A consumer can choose only between peanut b

Question

Perfect Complements: 3 Goods Case 3. A consumer can choose only between peanut butter, jelly, and bread. These goods are perfect comple- ments, and the consumer prefers to have exactly 2 slices of bread and 3 tablespoons of peanut butter for every 2 tablespoons of jelly. The utility function that represents these preferences is U(s, b,j mi3, , where s is the number of slices of bread, b is the number of tablespoons of peanut butter, and j is the number of tablespoons of jelly. The prices for the three goods are ps-1, pb-4, and p,- 2. The consumer has $100 to spend a) What is the consumer's budget constraint? b) What is the optimal consumption bundle? c) What is U(s,b',j)?

Explanation / Answer

Ans a)

Budget Constraint will b equal to

sumof (Priceof Commodity* Quantity of Commodity)<=Income

Ps*s+Pb*b+Pj*j<=100

1*s+4*b+2*j<=100

s+4b+2j=100 this is the equation for budget constraint

Ans b)

Optimal Consumption bundle is a unique point where

s/2=b/3 and s/2=i/2.....( Use this condition when solving for complement goods stuff)

b=3s/2 and s=j

We can use these into budget constraint

s+4(3s/2)+2(s)=100

s+6s+2s=100

9s=100

hence s*=100/9 and b*=3s/2=3(100/9)/2=100/6 j*=100/9

Ans c)

U(s*,b*,j*)=min(s*/2,b*/3,j*/2)=min(100/18,100/18,100/18)=100/18

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