Question

Josh only spends his discretionary money ($210) on chocolate

truffles (priced at $9a box) and comic books (p=$3 per comic book). His utility

function is of the Cobb-Douglas form with a=0.3

1.

Write the new budget constraint for Josh and his utility function.

2.

What is the marginal rate of substitution between chocolate truffles and comic

books for Josh?

3.

Solve for his optimal consumption bundle.

Utility Function: Q1^0.3 Q2^0.7

Budget Constraint: 9Q1+3Q2=210

Answer 1

We have the following information

Utility Function: Q1^0.3 Q2^0.7 where Q1 = chocolate truffles and Q2 = comic books

Budget Constraint:

1.The budget constraint is 9Q1 + 3Q2 < or = 210

2. Marginal rate of substitution = -MUQ1/MUQ2 = -0.3Q1^-0.7 Q2^0.7 / 0.7Q1^0.3 Q2^-0.3 = -3Q2/7Q1

3. At the optimal consumption bundle, |MRS| = P1/P2

3Q2/7Q1 = 9/3

Q2 = 7Q1

Use this in the budget equation 9Q1 + 3*7Q1 = 210

30Q1 = 210 or Q1* = 7 units and Q2* = 7*Q1* = 7*7 = 49 units

Optimal bundle is (7 chocolate truffles, 49 = comic books)