Question

Cost functions, a part of the definition of profit, are useful to gauge the performance of the business. Suppose an economist estimated that the cost function of a single-product firm as: C(Q) = 2 + 2Q + 2Q2 Based on this information, determine the followings and show all steps (first, you must define each of the terms in the cost function, and then plug in the numbers to have your answers; not just the answers): Hint: The use of Graphs is recommended. a. Define fixed cost and offer an example. Next, compute the fixed cost of producing 4 units of output using the cost function above. b. Define variable cost and offer an example. Next compute the variable cost of producing 4 units of output using the cost function above. c. Define total cost and then compute the total cost of producing 4 units of output using the cost function above d. Define and compute the average fixed cost of producing 10 units of output e. Define and compute the average variable cost of producing 10 units of output f. Define and compute the average total cost of producing 10 units of output g. Define marginal cost an offer an example. Next, compute the marginal cost when Q = 2, using the cost function above

Answer 1

a) Fixed cost is the cost that remains unchanged with each of the level of output. Expenses like rent, insurance, payment of loan are example of fixed cost. here the cost function is C= 2 + 2 Q + 2 Q ²

The fixed cost = 2. It does not affected by the unit of output produced.

b. Variable cost is the cost that changes with the change in output. Example of variable cost includes the cost of raw materials and packaging.

In the given cost function variable cost = 2Q + 2Q²

if the output is 4 unit then variable cost = (24)+(2 16) = 40 unit

c. Total cost is the sum of  Fixed cost and variable cost.

The total cost for producing 4 unit of output = fixed cost + Variable cost at 4 unit of output = 2 + 40 = 48 unit.

d. Average fixed cost is the amount of fixed cost for per unit of output.

AFC = TFC/Q

for 10 unit of output the average fixed cost = 2/10 =0.2

e. Average variable cost is defined as the total variable cost for each unit of output.

The total variable cost for 10 unit of output = (210) + (2100) = 220

Therefore the Average variable cost for 10 unit of output = 220/10 =22 unit.

f. The average total cost is the total cost per unit of output

The total cost for 10 unit of output = 2 + 220 = 222

Therefore, the average total cost for 10 unit of output = 222/10 = 22.2

g. marginal cost is the additional cost for producing one additional unit of output. For example, suppose the cost for producing 5 unit of output of a good is $50 and the cost for producing 6 unit of that good is $ 70. Therefore, the marginal cost =$10

   Here, C= 2 + 2 Q + 2 Q ²

Marginal cost = dC/dQ = 2+4Q

Now when Q=2, MC = 2+8 =10 unit