Question

Q3 . A cost function for a beef production business is give below;

TC = 100 + 3y – 0.2y2 + 0.04y3

a. From the above cost function, derive the exact equation for;

i. Marginal Cost (MC)

ii. Average Cost (AC)

b. Using the above cost function, calculate;

i. Total Fixed Cost

ii. Total Variable Cost

iii. Total Marginal when Y = 4

iv. Level of output Y when Average Variable Cost is at minimum.

Answer 1

ai) Marginal Cost : The Marginal Cost (MC) at Y items is the cost of producing the next item. It's formula is given as the following-

aii) Average Cost : The Average Cost (AC) for Y items is the total cost divided by Y. It's formula is given as the following :

b i) Total Fixed Cost : The Fixed Cost (FC) is the amount of money you have to spend regardless of how many items you produce. It is the component of the fixed cost which doesn't depend on the output produced, thus here :

b ii) Total Variable Cost: The Total Variable Cost (TVC) for Y items is the amount of money you spend to actually produce them. Thus, it depends on the output produced.

TC= TFC + TVC

b iii) Marginal Cost (Y=4)

Substituting Y= 4 in the above equation, we get: