Suppose that the demand curve for beans is given by:
Q=20-P
Where Q is thousands of pounds of beans bought per week and P is the price in dollars per pounds
a. How many beans will be bought at P=0
b. At what price does the quantity demanded of beans become zero
c. Calculate the total revenue for beans for each whole dollar price between the prices identified in parts a and b
d. What prices for beans yields the highest total revenue
20 thousand
20 dollars per pound
400000
5
To answer these questions, we will use the given demand equation Q = 20 - P, where Q represents the quantity of beans (in thousands of pounds) and P represents the price (in dollars per pound).
a. To find the quantity of beans bought at P = 0, we substitute P = 0 into the demand equation:
Q = 20 - 0
Q = 20
Therefore, 20 thousand pounds (or 20,000 pounds) of beans will be bought when the price is $0.
b. To find the price at which the quantity demanded of beans becomes zero, we set Q = 0 and solve for P:
0 = 20 - P
Rearranging the equation, we get:
P = 20
Therefore, the quantity demanded of beans becomes zero when the price is $20 per pound.
c. To calculate the total revenue for each whole-dollar price between $0 and $20, we need to multiply the quantity (Q) by the price (P) for each price level:
For P = $0:
Q = 20 - 0 = 20 thousand pounds
Total revenue = Q * P = 20 * 0 = $0
For P = $1:
Q = 20 - 1 = 19 thousand pounds
Total revenue = Q * P = 19 * 1 = $19 thousand
For P = $2:
Q = 20 - 2 = 18 thousand pounds
Total revenue = Q * P = 18 * 2 = $36 thousand
Continuing this process for each whole-dollar price between $0 and $20, we can calculate the total revenue at each price level.
d. To determine the prices that yield the highest total revenue, we need to compare the total revenue values calculated in part c. The price that yields the highest total revenue will correspond to the highest revenue value.
From the calculations in part c, we can observe the following total revenue values for each whole-dollar price between $0 and $20 (in thousand dollars):
P = $0: Total revenue = $0
P = $1: Total revenue = $19
P = $2: Total revenue = $36
...
We can continue this process for each price and compare the revenue values. The price that yields the highest total revenue will correspond to the price with the highest revenue value.