Average Total Cost Equation in Economics
What is the average total cost equation?
a. ATC = 4500Q + 5
b. ATC = 4500 + 10Q
c. ATC = 4500/Q+ 5
d. ATC = 4500/Q + 5Q
Answer:
The correct answer is (b) ATC = 4500 + 10Q.
In economics, the average total cost (ATC) is the sum of all the costs of production (fixed and variable) divided by the quantity of output produced. It is expressed as:
ATC = TC/Q
where TC is total cost and Q is quantity.
Given the equations TC = 4,500 + 5Q^2 and MC = 10Q, we can find the average total cost as follows:
First, let's find the average variable cost (AVC), which is total variable cost divided by the quantity of output produced.
Since MC = 10Q, MC is equal to the change in TVC over the change in Q:
MC = ΔTVC/ΔQ ⇒ 10Q = ΔTVC
Therefore, total variable cost (TVC) is calculated as:
TVC = ∫ MC dQ = 10Q^2/2 = 5Q^2
The average variable cost (AVC) is then:
AVC = TVC / Q = 5Q / Q = 5
Next, we find the total fixed cost (TFC) and average fixed cost (AFC), leading to the correct answer of (b) ATC = 4500 + 10Q.