Green et al. (2005) estimate the supply and demand curves for California process
ID: 1154328 • Letter: G
Question
Green et al. (2005) estimate the supply and demand curves for California processed tomatoes. The supply function is: In(Qs) - 0.200 +0.550 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(Od) 2.600-0.200 In(p)0.150 In(pt), where pt is the price of tomato paste (which is what processing tomatoes are used to produce) in dollars per ton. Suppose pt $130. Determine how the equilibrium price and quantity of processing tomatoes change if the price of tomato paste rises by 22%. If the price of tomato paste rises by 22%, then the equilibrium price will V by $. (Enter a numeric response using a real number rounded to two decimal places.)Explanation / Answer
Ln(Qs) = Ln(Qd)
0.2+0.550*(ln(p)) = 2.6-0.2*ln(p)+0.15*ln(130)
0.2+0.550*(ln(p)) =2.6-0.2*ln(p)+0.15*4.87=2.6-0.2*ln(p)+0.73 = 3.3-0.2*ln(p)
0.2+0.550*(ln(p))+0.2*ln(p) = 3.3-0.2 =3.13
0.550*(ln(p))+0.2*ln(p) = 3.13
0.75ln(p) =3.13
Solving for p = 65
Now for an increase in tomato paste by 22%,
We have, Pt = 158.6
0.2+0.550*(ln(p)) = 2.6-0.2*ln(p)+0.15*ln(158.6)
0.2+0.550*(ln(p)) =2.6-0.2*ln(p)+0.15*5.07=2.6-0.2*ln(p)+0.76 = 3.36-0.2*ln(p)
0.2+0.550*(ln(p))+0.2*ln(p) = 3.36-0.2 =3.2
0.550*(ln(p))+0.2*ln(p) = 3.2
0.75ln(p) =3.2
Solving for p = 72
So, if the price of tomato rises by 22%, then the equilibrium price will be $72 by $7
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