A firm has fixed costs of

A firm has fixed costs of 200 each week, and the variable costs per unit can be expressed by the function, VC=8Q-10.



1. Find an expression for the total cost function and show that the average cost function is given by



AC=200/Q 8Q-10



2. Find the level of output that minimises AC. What is the minimum value of AC?



3. Find an expression for the marginal cost function and verify that marginal cost

is equal to average cost at this output level.
(I wanna tell this first: the variable costs per unit should be called as AVC - average variable costs, not VC. So it should be: AVC = 8Q - 10)

1. We have: FC = 200

AVC = 8Q - 10, hence VC = AVC x Q = 8Q^2 - 10Q

Total costs are the sum of fixed costs and variable costs, so: TC = FC VC = 8Q^2 - 10Q 200

Average cost function should be: AC = TC/Q = 200/Q 8Q - 10

2. We have to find Q so that AC min.

According to Cauchy