ECON101 Lecture 8: Quotas
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A mathematical demand function for new Toyotas sold per year for a dealer is as follows Qr = 200 - 0.001Pt + 0.005Pm - 10Pg + 0.01I +0.003A
where
Qt = quantity purchased,
Pt = the average price of Toyotas,
Pm = the average price of mazdas,
Pg = the price of gasoline,
I = per capita income, and
A = dollars spent annually on advertising
PM = $20000 PG = $1.00 I = $15000 A = $10000
1. Use the above to calculate the arc price elasticity of demand between PT = $15000 and PT = $10000
2. What will the estimated quantity sold and total revenue be at each of the above prices (fill in the table below)?
PT |
QT |
Revenue |
$15000 |
||
$10000 |
3. Marketing wants to lower PT from $15000 to $10000. From a revenue viewpoint, explain why you agree or disagree with Marketing. Look at the elasticity calculated in #1 and the behavior of revenues in #2.
4. Calculate the point price elasticity of demand, given that PT = $12500 and QT = 345. Compare the results with the answer to #1. If the results are the same, why does this make sense? If the results differ, why does this make sense? The formula is:
5. Calculate the point cross-price elasticity of demand between gasoline price (PG) and Toyota demand. Assume the OPEC lowered petroleum production quotas and caused the price of gasoline to triple to PG = $3.00. Calculate a new QT for PG = $3.00 and PT = $15000. Other variables and their values are given at the top, before question #1. Explain what this elasticity value implies for the responsiveness of the demand for Toyotas is relative to the price of gasoline?
1. What is price elasticity of demand when prices increase from $3 to $4 and quantity decrease from 90 cups to 70 cups?
2. Suppose that business travelers and vacationers have the following demand for airline tickets from New York to Boston:
Price | Quantity Demanded by Business | Quantity Demanded by Vacationers |
150 | 2100 | 1000 |
200 | 2000 | 800 |
250 | 1900 | 600 |
300 | 1800 | 400 |
As the price of tickets rises from $200 To $250, what is the price elasticity of demand for a) business travelers and b) vacationers? Use the midpoint method to calculate. Why might vacationers have a diffeent elasticity from business travelers?
3. How can sellers utilize the price elasticity of demand for maximum total revenue?