Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / Cost functions, a part of the definition of profit, are useful to gauge the performance of the business
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)=40+4Q+4Q2+4Q3C(Q)=40+4Q+4Q2+4Q3
Based on this information, determine the followings and show all steps.
a. Define fixed cost and offer an example. Next, compute the fixed cost of producing 10 units of output using the cost function above,
b. Define variable cost and offer an example. Next compute the variable cost of producing 10 units of output using the cost function above,
c. Define total cost and then compute the total cost of producing 10 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=10Q=10, using the cost function above.
a.
Fixed cost is the cost of production, where the fixed payment is made either periodical or lump sum. The example is bills, rent of land or place, which do not relate to output.
FC=40FC=40
b.
Variable cost relates to output, unlike fixed cost. The Variable cost varies according to change in output. Hence more the output more the cost. For example, the raw material cost, the cost of per unit taxation.
VC=4Q+4Q2+4Q3=4440VC=4Q+4Q2+4Q3=4440
c.
Total cost is combination of both Variable cost and fixed cost. Hence all the cost of production, from bills, rents, advertising, operational expenses and raw material are part of total cost.
TC=40+4(10)+4(10)2+4(10)3=4480TC=40+4(10)+4(10)2+4(10)3=4480
d.
Average fixed cost is calculated fixed with every unit of output. For example, if fixed cost of all production is 100, average fixed cost is cost with every produced unit, say 4, then AFC is 25. For example, if fixed cost includes rental cost, then AFC is cost of rent for every unit.
AFC=Q=4010=4AFC=Q=4010=4
e.
Average variable cost is calculated variable cost with every unit of output. For example, if variable cost of all production is 100, then average variable cost is cost with every produced unit, say 4, then AVC is 25. For example, if variable cost includes raw material cost, then AVC is cost of raw material for every unit.
AVC=Q=444010=444AVC=Q=444010=444
f.
Similarly, Average total cost is calculated total cost with every unit of output. For example, if total cost of all production is 100, then average total cost is cost with every produced unit, say 5, then ATC is 20.
ATC=Q=448010=448ATC=Q=448010=448
g.
Marginal cost is total cost added with every unit. Rather than considering gross cost for all units produced, we see only the additional part of cost with every one unit. For example, if my total cost is 100, in Marginal cost, I would only see, if after 1 unit produced, how much MC is added, after 2nd unit, how much MC is added and so on.
MC=(TC)′=(40+4Q+4Q2+4Q3)′=4+8Q+12Q2=4+8(10)+12(10)2=1284
