Quantitative Question Consider a situation where a firm that

Quantitative Question Consider a situation where a firm that produces compost is trying to figure out how its costs are structured. No matter what, the firm must pay 100,000 per year in licensing fees to the state. On top of that, for every 5,000 units of compost they produce, they require an additional storage bin, which costs the firm 3,000. Lastly, the firm must pay a laborer 2 per unit of compost produced (a) Identify which costs are fixed, and which are variable. Explain your reasoning. (Hint: Think carefully.) (b) For quantities between 6,000 and 8,000 units, what is the total cost function? (c) From your result in part (b), derive the average total cost, average variable cost and average fixed cost functions.

Solution

A) Fixed costs are the cost that has to be paid no matter what and is not dependent on the quantity produced. Here, the firm licensing fees has to be paid every year (i.e 100,000 per year) which is the fixed cost.

Variable cost is the cost that changes according to the quantity produced. Here,labor cost and storage bin cost that increases when 5000 units are produced will be termed as variable cost.

B) Total cost is the sum of fixed cost and variable cost

Here, Licensing fee + storage bin cost + labor cost

For 6000 quantity

I.e 100000+3000+3000 (as the quantity exceeds 5000 units)+ 6000*2

-118000 ( for 6000 units)

for 8000 units

100000+6000+8000*2

-122000

Therefore it will lie between 118000 to 122000.

C) Average total cost is total cost divided by quantity

for 6000 units = 118000/6000= 19.6

Average variable cost = VC/Q = 18000/6000= 3

Average fixed cost = FC/Q = 100000/6000= 16.6