Question

1. 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) John wants to choose the bundle $(R,C)$ that maximizes his utility subject to the budget constraint.

$Max_{10R^2C}\ S.t\ 180\ge20R+10C$

(b) The Utility function is of the Cobb-Douglas type. The optimum bundle satisfies the slope condition and is also on the budget line.

Slope condition$\frac{MU_R}{MU_C}=\frac{P_R}{P_C}\implies\frac{2C}{R}=2\\$

Budget line $180=20R+10C\implies20R+10R=180\implies30R=180R^*=6,C^*=6$

6 chicken wings and 6 chicken ribs

(c)$2C/R= PR/10 ⟹ C=PRP/20$

$180=PR+10PRR+1/2PRP$

$180=6PRR/2=180=P(PR)=60/PR$

=60/PR

(d) Normal, this is because demand increases as income increases.