a firm faces the following. TC= 100-20Q+3Q^2 , TR=60Q-2Q^2 . Find (i) TFC , (ii) AC , (iii) AVC , (iv) MC , (v) AR , (vi) MR

1 500

2 80

To find the answers to the given questions, we need to understand the definitions of the terms used in the context of microeconomics. Here are the steps to find each of the variables:

(i) Total Fixed Cost (TFC):
Total Fixed Cost (TFC) refers to the cost that does not vary with the level of output. In the given cost equation TC = 100 - 20Q + 3Q^2, the term 100 represents the fixed cost. Hence, TFC = $100.

(ii) Average Cost (AC):
Average Cost (AC) refers to the total cost per unit of output. To find AC, we divide the total cost (TC) by the quantity (Q):
AC = TC / Q

In this case, TC = 100 - 20Q + 3Q^2. So, AC = (100 - 20Q + 3Q^2) / Q.

(iii) Average Variable Cost (AVC):
Average Variable Cost (AVC) refers to the variable cost per unit of output. To calculate AVC, we divide the total variable cost (TVC) by the quantity (Q):
AVC = TVC / Q

Since TVC is the difference between TC and TFC, AVC = (TC - TFC) / Q, where TFC is given as $100.

(iv) Marginal Cost (MC):
Marginal Cost (MC) refers to the additional cost incurred by producing one additional unit of output. To find MC, we differentiate the total cost function (TC) with respect to quantity (Q):
MC = dTC / dQ

In this case, TC = 100 - 20Q + 3Q^2. Taking the derivative of TC with respect to Q, we get MC = -20 + 6Q.

(v) Average Revenue (AR):
Average Revenue (AR) refers to the total revenue per unit of output. To find AR, we divide the total revenue (TR) by the quantity (Q):
AR = TR / Q

In this case, TR = 60Q - 2Q^2. So, AR = (60Q - 2Q^2) / Q.

(vi) Marginal Revenue (MR):
Marginal Revenue (MR) refers to the additional revenue earned by selling one additional unit of output. To calculate MR, we differentiate the total revenue function (TR) with respect to quantity (Q):
MR = dTR / dQ

In this case, TR = 60Q - 2Q^2. Taking the derivative of TR with respect to Q, we get MR = 60 - 4Q.

By following these steps, you can calculate each of the variables as necessary.