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.