Question

In: Economics

The Economic Research Service of the U.S. Department of Agriculture has reported the results of a...

The Economic Research Service of the U.S. Department of Agriculture has reported the results of a study of the effects of the price of various types of oranges on the quantity demanded of the oranges. The oranges are sold in perfectly competitive markets. In particular, three types of oranges were studied: 1) Florida Valencia, 2) California Navel, and 3) California Blood Orange. In nine test stores in Grand Rapids, Michigan, the researchers varied the price of each of these types of oranges for a month. The effect of a 1% increase in the price of each type of orange on the rate of purchase of this and each of the other types of oranges is shown below.

…results in the following percentage change in the quantity demanded of:

A 1% increase in the price of:

Florida Valencia

California Navel

California Blood Orange

Florida Valencia

-3.1

+1.6

+0.01

California Navel

+1.2

-3.0

+0.1

California Blood Orange

+0.2

+0.1

-2.8

(a) What is the value of the estimated price elasticity of demand for each type of orange? Explain.

(b) What is the cross-price elasticity of demand for each pair of different types of oranges? (i.e. the cross price elasticity of demand for California Navel with respect to the price of Florida Valencia, etc.) Explain.

(c) How can you tell from the estimates that that each pair of oranges are substitutes for one another?

(d) What types of oranges seem to be the closest (strongest) substitutes for one another? Explain.

(e) Is this useful information for the members of the California Orange Association Cooperative trade association and the members of the Florida Orange Growers trade association? Are there any limitations of the results of the study? Briefly explain.

Solutions

Expert Solution

a). So, there are three types of oranges and the own price elasticity and the cross price elasticity of demand for these oranges are given in the table. So, the elasticity of demand of “Florida Valencia” is “-3.1”, => as the price of “Florida Valencia” increases by “1%” the quantity demanded of “Florida Valencia“ decreases by “3.1%”. Similarly, the elasticity of demand of “California Navel” is “-3”, => as the price of “California Navel” increases by “1%” the quantity demanded of “California Navel“ decreases by “3%”. Finally, the elasticity of demand of “California blood orange” is “-2.8”, => as the price of “California blood orange” increases by “1%” the quantity demanded of “California blood orange “ decreases by “2.8%”

b).

Now, the cross price elasticity of demand for “Florida Valencia” with respect to the price of “California Navel” is “1.2”, => as the price of “California Navel” increases by “1%” the demand for “Florida Valencia” increases by “1.2%”. Similarly, the cross price elasticity of demand for “Florida Valencia” with respect to the price of “California blood orange” is “0.2”, => as the price of “California blood orange” increases by “1%” the demand for “Florida Valencia” increases by “0.2%”.

The cross price elasticity of demand for “California Navel” with respect to the price of “Florida Valencia” is “1.6”, => as the price of “Florida Valencia” increases by “1%” the demand for “California Navel” increases by “1.6%”. Similarly, the cross price elasticity of demand for “California Navel” with respect to the price of “California blood orange” is “0.1”, => as the price of “California blood orange” increases by “1%” the demand for “California Navel” increases by “0.1%”.

The cross price elasticity of demand for “California blood orange” with respect to the price of “Florida Valencia” is “0.01”, => as the price of “Florida Valencia” increases by “1%” the demand for “California blood orange” increases by “0.01%”. Similarly, the cross price elasticity of demand for “California blood orange” with respect to the price of “California Navel” is “0.1”, => as the price of “California Navel” increases by “1%” the demand for “California blood orange” increases by “0.1%”.

c).

We can see that all the cross price elasticity of demand are positive, => they all are substitute to each other, => if the price one increases by “1%”, => the quantity demanded of other will increases, => they are substitute to each other.

d).

Now, according to the given report “Florida Valencia” and “California Navel” are closed substitute to each other having largest “cross price elasticity of demand”.

e).

So, in the given report we have given the estimated value of “own price elasticity of demand” and the “cross price elasticity of demand” of three different types of oranges. So, of course these estimated detail are useful to these associations, but as we also know that the “demand for orange” also influence by the price of other fruits. So, if the report content the “cross price elasticity of demand for these oranges” with respect to other fruits as well then that would have been more useful to these associations.

So, these reports are perfect as all the “own price elasticity of demand” are “negative” and “cross price elasticity” are positive.


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