Calculate the firm's (I) variable cost at output level 2, 4 and 6 (Ii) marginal cost at output level 2 and 6 (Iii) average cost at output level 2 and 3?

To calculate the firm's variable cost at output levels 2, 4, and 6, we need to know the total cost and fixed cost at each output level.

Let's assume the total cost and fixed cost at output levels 2, 4, and 6 are as follows:
Output level 2:
Total cost = $100
Fixed cost = $50

Output level 4:
Total cost = $200
Fixed cost = $50

Output level 6:
Total cost = $300
Fixed cost = $50

(I) Variable cost at output level 2, 4, and 6:
Variable cost = Total cost - Fixed cost

At output level 2:
Variable cost = $100 - $50 = $50

At output level 4:
Variable cost = $200 - $50 = $150

At output level 6:
Variable cost = $300 - $50 = $250

(II) Marginal cost at output level 2 and 6:
Marginal cost is the additional cost incurred by producing one more unit of output.

Marginal cost at output level 2:
MC = Change in total cost / Change in output
MC = ($200 - $100) / (4 - 2) = $50

Marginal cost at output level 6:
MC = Change in total cost / Change in output
MC = ($300 - $200) / (6 - 4) = $50

(III) Average cost at output level 2 and 3:
Average cost is the total cost divided by the output level.

Average cost at output level 2:
AC = Total cost / Output
AC = $100 / 2 = $50

Average cost at output level 3:
AC = Total cost / Output
AC = $150 / 3 = $50

Therefore, the firm's variable cost at output level 2, 4, and 6 is $50, $150, and $250 respectively. The marginal cost at output level 2 and 6 is $50, and the average cost at output level 2 and 3 is $50.

Given Information:

- Total cost function: TC = 2Q^2 + 4Q + 6
- Output levels: 2, 4, and 6

(I) Variable Cost:

Variable cost is equal to total cost minus fixed cost. The fixed cost in this case is 6.

- Output level 2: Variable cost = TC - Fixed cost = 2(2)^2 + 4(2) + 6 - 6 = 14
- Output level 4: Variable cost = TC - Fixed cost = 2(4)^2 + 4(4) + 6 - 6 = 46
- Output level 6: Variable cost = TC - Fixed cost = 2(6)^2 + 4(6) + 6 - 6 = 98

(II) Marginal Cost:

Marginal cost is the change in total cost divided by the change in output.

- Output level 2 to 6: Marginal cost = (TC6 - TC2) / (Q6 - Q2) = (98 - 14) / (6 - 2) = 27

(III) Average Cost:

Average cost is the total cost divided by the output level.

- Output level 2: Average cost = TC / Q = (2(2)^2 + 4(2) + 6) / 2 = 13
- Output level 3: Average cost = TC / Q = (2(3)^2 + 4(3) + 6) / 3 = 11