Question

Question 2 [E3.3] Green et al. (2005) estimated the supply and demand curves for California processing tomatoes. The supply function is In Q = 0.2 +0.55 In P where Q is the quantity of processing tomatoes in millions of tons per year, and Pis the price in dollars per ton. The demand function is in Q = 2.6 - 0.3 In P+0.5 In P, where Pris the price of tomato paste (which is what processing tomatoes are used to produce) in dollars per ton. In 2002. P, = $110. (a.] What is the reduced demand function for processing tomatoes (that is, the function where quantity demanded is a function of the price of processing tomatoes)? [b.] How does the quantity of processing tomatoes vary with the price? [c.] What is the price elasticity of demand, and the price elasticity of supply, for processing tomatoes? Given these calculations, what can you say about the demand, and the supply of processing tomatoes?

Answer 1

Solution:

Supply function: In Q = 0.2 + 0.55*ln P

Demand function: ln Q = 2.6 - 0.3*ln P + 0.5*ln Pt

a) With Pt = $110, reduced demand function becomes:

ln Q = 2.6 - 0.3*ln P + 0.5*ln(110)

ln Q = 2.6 - 0.3*ln P + 2.35

ln Q = 4.95 - 0.3*ln P

b) Quantity of processing tomatoes vary differently for demand and supply function. For demand function, quantity of processing tomatoes decrease with increase in price, and as per the equation, a percent increase in price decreases quantity demanded by 0.3%.

For supply function, quantity of processing tomatoes increase with increase in price, and as per the equation, a percent increase in price increases quantity demanded by 0.55%.

c) Price elasticity = percentage change in quantity/percentage change in price

As already seen in part (b), for a log-log model, coefficient determines by what percentage dependent variable change with a percentage change in independent variable.

So, price elasticity of demand = -0.3

Price elasticity of supply = 0.55

So, both demand and supply are inelastic (as their absolute values are lower than 1).