Question

Green et al. (2005) estimate the supply and demand curves for California processed tomatoes. The supply function is: In(Os) 0.2000.550 In(p) where Q is the quantity of processing tomatoes in millions of tons per year and p is the price in dollars per ton. The demand function is In(Q)-2.600 0.200 In(p) + 0.150 In(pt). where p, is the price of tomato paste (which is what processing tomatoes are used to produce) in dollars per ton Suppose pt $128. Determine how the equilibrium price and quantity of processing tomatoes change if the price of tomato paste falls by 15%. If the price of tomato paste falls by 15%, then the equilibrium price will by $. (Enter a numeric response using a real number rounded to two decimal places.)

Answer 1

ln(Qd) = 2.6 - 0.2 ln(p) + 0.15 ln(pt)

When pt = 128,

ln(Qd) = 2.6 - 0.2 ln(p) + 0.15 ln (128)

ln(Qd) = 2.6 - 0.2 ln(p) + 0.15 x 4.85

ln(Qd) = 2.6 - 0.2 ln(p) + 0.73

ln(Qd) = 3.328 - 0.2 ln(p)

Equating with supply,

3.328 - 0.2 ln(p) = 0.2 + 0.55 ln(p)

0.75 ln(p) = 3.08

ln(p) = 4.107

p = e^4.107 = 60.76

When pt falls by 15%, value of pt = 128 x 0.85 = 108.8

ln(Qd) = 2.6 - 0.2 ln(p) + 0.15 ln (108.8)

ln(Qd) = 2.6 - 0.2 ln(p) + 0.15 x 4.69

ln(Qd) = 2.6 - 0.2 ln(p) + 0.703

ln(Qd) = 3.303 - 0.2 ln(p)

Equating with supply,

3.303 - 0.2 ln(p) = 0.2 + 0.55 ln(p)

0.75 ln(p) = 3.103

ln(p) = 4.138

p = e^4.138 = 62.68

Equilibrium price will increase by 1.92 (= 62.68 - 60.76).