Assuming the inverse demand function for good Z can be written as P = 90 - 3Q, when Q is equal to 5, average revenue and marginal revenue are equal to ________ and ________.
Choose one answer.
a. $75; $75.
b. $75; $60.
c. $60; $60.
d. $85; $85.
b. $75; $60.
To find the average revenue and marginal revenue when Q is equal to 5, we first need to understand the formulas for average and marginal revenue.
Average Revenue (AR): Average revenue is the total revenue (TR) divided by the quantity (Q). Mathematically, AR = TR / Q.
Marginal Revenue (MR): Marginal revenue is the change in total revenue (ΔTR) resulting from a change of one unit in quantity (Q). Mathematically, MR = ΔTR / ΔQ.
Now let's calculate the average and marginal revenue when Q is equal to 5.
1. Average Revenue (AR):
To find AR, we need to calculate the total revenue (TR) when Q is equal to 5. TR is calculated by multiplying the price (P) by the quantity (Q). In this case, we have the inverse demand function P = 90 - 3Q. Let's substitute Q = 5 into the inverse demand function to find the price (P) at this quantity:
P = 90 - 3(5)
P = 90 - 15
P = 75
Now, we can calculate AR by dividing TR by Q:
AR = TR / Q = (P * Q) / Q = P = 75
So, the average revenue is $75.
2. Marginal Revenue (MR):
To find MR, we need to calculate the change in total revenue (ΔTR) resulting from a change of one unit in quantity (ΔQ). In this case, we will compare the total revenue at Q = 5 to the total revenue at Q = 4.
Total revenue at Q = 5:
TR(Q=5) = P * Q = 75 * 5 = 375
Total revenue at Q = 4:
TR(Q=4) = P * Q = (90 - 3(4)) * 4 = 78 * 4 = 312
ΔTR = TR(Q=5) - TR(Q=4) = 375 - 312 = 63
ΔQ = 5 - 4 = 1
Now we can calculate MR using the formula MR = ΔTR / ΔQ:
MR = ΔTR / ΔQ = 63 / 1 = 63
So, the marginal revenue is $63.
Therefore, the correct answer is:
b. $75; $63.
To find the average revenue when Q is equal to 5, we need to find the total revenue and then divide it by Q.
Total Revenue is given by TR = P * Q, where P is the price and Q is the quantity.
Given the inverse demand function P = 90 - 3Q, we can substitute Q = 5 to find the price at that quantity.
P = 90 - 3(5)
P = 90 - 15
P = 75
Therefore, the price when Q is equal to 5 is $75.
To find the total revenue, we multiply the price by the quantity.
TR = P * Q
TR = $75 * 5
TR = $375
The average revenue is TR / Q.
Average Revenue = $375 / 5
Average Revenue = $75
Now let's find the marginal revenue.
Marginal Revenue (MR) is the change in total revenue when the quantity changes by one unit.
To find the change in total revenue, we can subtract the total revenue at Q = 5 from the total revenue at Q = 4.
Total revenue at Q = 4:
TR1 = P * Q
TR1 = (90 - 3(4)) * 4
TR1 = (90 - 12) * 4
TR1 = 78 * 4
TR1 = $312
Total revenue at Q = 5:
TR2 = P * Q
TR2 = (90 - 3(5)) * 5
TR2 = (90 - 15) * 5
TR2 = 75 * 5
TR2 = $375
Change in total revenue (ΔTR) = TR2 - TR1
ΔTR = $375 - $312
ΔTR = $63
Therefore, the marginal revenue when Q is equal to 5 is $63.
The correct answer is b. $75; $63.