Question

Assume that the cost function for a firm is equal to C(Q) = 1000 + 5Q + 10Q² and the Marginal Cost function is MC(Q) = 5 + 20Q.

What is the level of fixed cost when production is equal to 100? 200?

What is the level of variable cost when production is equal to 100? 200?

What is the level of Average Fixed Cost when production is equal to 100? 200?

What is the level of Average Variable Cost when production is equal to 100? 200?

What is the level of Average Total Cost when production is equal to 100? 200?

What is marginal cost when production is equal to 100? 200?

Answer 1

1) Fixed cost is the cost which does not change with change in output i.e. 1000.

Fixed cost remains same at each level of production so Fixed cost at 100 or 200 units is $ 1000

2) Variable cost is the cost which changes with change in output.

VC = 5Q + 10Q²

VC(100) = 5(100) + 10(100)² = 500 + 100000 = 100500

VC(200) = 5(200) + 10(200)² = 1000 + 400000 = 401000

3) AFC = FC/Q

AFC(100) = 1000/100 = 10

AFC(200) = 1000/200 = 5

4) AVC = VC/Q

AVC(100) = 100500/100 = 1005

AVC(200) = 401000/200 = 2005

5) ATC = TC/Q

ATC(100) = (1000 + 100500)/100 = 101500/100 = 1015

ATC(200) = (1000 + 401000)/200 = 402000/200 = 2010

6) MC = 5 + 20Q

MC(100) = 5 + 20(100) = 2005

MC(200) = 5 + 20(200) = 4005