Illustrate the relation between Marginal Cost (MC), Average Total Cost (ATC), Average Variable Cost (AVC) and Average Fixed Cost (AFC) curves. Given a total cost function,
TC(Q) = 7Q2 + 5Q + 75
where Q represents quantity of output produced. Find the expression for Variable cost
(VC), Fixed cost (FC), AVC, AFC and ATC.
Answers
Explanation:
Cost refers to the obligation incurred by the firm for producing any given level of output.
Explanation:
Now we will discuss various types of costs and their relationships .
AVERAGE FIXED COST: The average fixed cost is the per unit cost of the fixed factors. It is obtained by dividing the total fixed cost with the total unit of output produced.
Symbolically AFC= TFC\div QAFC=TFC÷Q
The average fixed cost falls as the output increases because the numerator remains the same while the denominator increases. For the very small output average fixed cost is high and for large output it is low.
The slope of the AFC curve is downward from left to right showing continuous falls in average fixed cost as the output increases. The AFC curve never touches the x-axis average fixed cost cannot be zero.
AVERAGE VARIABLE COST :Average variable cost is the per unit cost of the variable factors of production.
Symbolically AVC= TVC\div QAVC=TVC÷Q
The average variable cost curve is the U-shaped. It means that the AVC curve first falls, reaches its minimum and then start rises. The u shape of AVC follows directly from law of variable proportion.
AVERAGE TOTAL COST : Average total cost or simply the average cost is the per unit cost of both the fixed and variable factors of production . It is obtained by dividing the total cost with the total unit of output.
Symbolically ATC= TC\div QATC=TC÷Q
Average total cost curve is the vertical summation of average fixed cost curve and average variable cost cost curves. It is U shaped which indicates the the if falls initially, reaches its minimum and then starts increasing.
MARGINAL COST : Marginal cost is the addition to total cost as one more unit of output is produced.
Symbolically MC= \Delta TC\div \Delta QMC=ΔTC÷ΔQ
Marginal cost curve is the U shaped. As the output increases the marginal cost curve slopes downward, reaches its minimum and then start sloping upward.
From the cost function in the question
Variable cost = 7Q^{2}+5Q7Q2+5Q
Fixed cost = 7575
Average variable cost = 7Q+57Q+5
Average fixed cost = 75\div Q75÷Q
Average total cost =7Q+5+75\div Q7Q+5+75÷Q