Answer to Question #188749 in Microeconomics for hguf

Question

Chicken (C) and pork (P) are substitutes. In the short run the quantity of chicken and

pig are assumed fixed at 100 and 200 respectively. Suppose their demand function are given

as

(a) What are the equilibrium price of chicken and pork?

(b)Suppose an outbreak of chicken disease causes quantity of chicken to

decline by half. How does this affect chicken and pork prices?

Answer 1

Chicken (C) and pork (P) are substitutes. In the short run, the quantity of chicken and pig are assumed fixed at 100 and 200 respectively. Suppose their demand functions are given as

$P_c = 900 -Q_c + 0.5P_p \\ P_p = 600 - Q_p + 0.5P_c$

(a) What are the equilibrium price of chicken and pork?

(b) Suppose an outbreak of chicken disease causes the quantity of chicken to decline by half. How does this affect chicken and pork prices?

(a)

$Q_c=100 \\ Q_p=200 \\ P_c=900-Q_c+0.5P_p \\ P_c=900-100+0.5P_p \\ P_c=800+0.5P_p \\ P_p=600-Q_p+0.5P_c \\ P_p=600-200+0.5P_c \\ P_p=400+0.5P_c \\ P_p=400+0.5(800+0.5P_p) \\ P_p=400+400+0.25P_p \\ 0.75P_p=800 \\ P_p=1066.67 \\ P_c=800+0.5P_p \\ P_c=1333.34$

(b)

$Q_c=50 \\ Q_p=200 \\ P_c=900-Q_c+0.5P_p \\ P_c=900-50+0.5P_p \\ P_c=850+0.5P_p \\ P_p=600-Q_p+0.5P_c \\ P_p=600-200+0.5P_c \\ P_p=400+0.5P_c \\ P_p=400+0.5(850+0.5P_p) \\ P_p=400+425+0.25P_p \\ P_p=\frac{825}{0.75} \\ P_p=1100 \\ P_c=850+0.5P_p \\ P_c=850+0.5(1100) \\ P_c=1400$