Answer to Question #210320 in Microeconomics for koya

Question

John likes pork Ribs (R) and Chicken wings (C). His utility function is U(R,C)=10\, R^2\, C

U(R,C)=10R2

C. His weekly income is 90

90 USD which he spends exclusively on R and C. The price for a slab of ribs is 10

10 USD and 5

5 USD for a piece chicken. Note that MU_R = 20\, R\, C

MUR

​=20RC and MU_C = 10\, R^2

MUC

​=10R2

. What is John's optimal bundle?

Answer 1

Solution:

John’s optimal bundle:

First derive the budget constraint or line:

I = PxX + PyY

I = P_RR + P_CC

Where: I = Weekly income = 90

            P_R = Price of Ribs = 10

            P_C = Price of chicken = 5

90 = 10R + 5C

Now derive the consumption bundle:

The consumption bundle that maximizes utility is one where the slope of the indifference curve $\frac{MU_{R} }{MU_{C}}$ is equal to the slope of the budget line $\frac{P_{R} }{P_{C}}$ in absolute value terms.

MU_R = 20RC

MU_C = 10R²

$\frac{MU_{R} }{MU_{C}} = \frac{P_{R} }{P_{C}}$

20RC/10R² = 10/5

2C = 2R

C = R

Substitute this into the budget line:

90 = 10R + 5C

90 = 10R + 5R

90 = 15R

R = $\frac{90 }{15} = 6$

R = 6

Since C = R, then C = 6

Th consumption bundle is 6 ribs and 6 chicken.

The consumption bundle that maximizes utility is U (_{R, C}) = (6, 6)