Answer to Question #169998 in Microeconomics for Don

Question

John likes chicken ribs and chicken wings. Her utility function is U(R,C) =10R2 C. Her weekly

income is 180 of which she spends exclusively on R and C. The price for the slab of ribs is 20

shillings and 10 for wings.

a. What is John’s problem?

b. What is John’s optimal bundle?

c. What is John’s demand function for ribs?

d. Are ribs a normal or inferior good?

Answer 1

a.). What is John’s problem?

Budget constraint:

Price of ribs (R) = 20

Price of wings (C) = 10

180 = 20R + 10C

b.). What is John’s optimal bundle?

U (_{R, C}) = 10R²C

MU_R = 20RC

MU_C = 10R²

MRS_RC = $\frac{MU_{R} }{MU_{C} }$ =$\frac{20RC }{10R^{2} }$ = $\frac{2C }{R }$

MRS = $\frac{P_{R} }{P_{C} }$

$\frac{2C}{R}$ = $\frac{20}{10}$

$\frac{2C}{R}$ = 2

C = R

Plug into the budget constraint:

180 = 20R + 10C

180 = 20R + (10$\times$R)

180 = 20R + 10R

180 = 30R

R =$\frac{180}{30}$ = 6

R = 6

C = 6

c.). What is John’s demand function for ribs?

180 = 20R + 10C

9 = R + 0.5C

R = 9 – 0.5C

d.). Ribs are a normal good. This is because as consumer's income rises, the demand for ribs increases.