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A frigid Florida winter is taking its toll on your sandwich. The sunshine state is the main U.S. source for fresh winter
tomatoes, and its growers lost some 70 percent of their crop during January’s prolonged cold weather. The average wholesale
price for a 25-pound box of tomatoes is now $30, up from $6.50 a year ago. Florida’s growers would normally ship about 25
million pounds of tomatoes a week; right now, they are shipping less than a quarter (8million). High demand has driven up
prices and wholesalers are buying from Mexico. Based on that, some restaurants provided tomatoes only on request.”
a. Using the information above find the demand and supply curves in the market for winter tomatoes.
b. Calculate the price elasticity of demand for winter tomatoes as well as elasticity of supply using the midpoint method.
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As I read this text, I become smiling.
Indeed, they write "8 millions pounds is less than a quarter of 25 millions pounds . . . ".
Millions blinded them. 8 millions pounds is not a quarter of 25 millions pounds:
8 millions pounds is about one third of 25 millions pounds.
So, these writers even are not able to call fractions correctly in their composition, using their proper names.
It tells me that I should not trust their words: I only can smile reading it.
Thus, I can not trust their words - I will use their numbers, instead.
Regarding for the numbers, I see the change in price from $6.50 to $30 and the change in quantity
from 25 millions pounds a week to 8 millions pounds a week.
So, I write the interpolation formula for the price 'p' of a 25-pound box as a function of the mass
of shipped production 'm'
P - 6.5 = = -1.382*(m-25),
or
P(m) = 6.5 - 1.382*(m-25) dollars for 25-pound box,
where m is the mass in million pounds of tomatoes shipped in a week.
This is the price function.
The demand function is the inverse function
m = + 25 = -0.723(P-6.5) + 25 million pounds of tomatoes shipped a week
for the price 'P' dollars of the 25-pound box.
So, I answered question (a).
When you solve such problems and use an interpolation formula, you should be
very accurate and place right numbers in proper places.