Answer :
Answer:
a) Average Cost function = 0.1 + (1000/x)
Marginal Cost function = 0.1
b) At x = a = 2000
Average Cost = 0.6
Marginal Cost = 0.1
c) The average cost calculate at x = 2000 in (b) represents the average cost of producing the first 2000 units of product and the marginal cost calculated at x = 2000 in (b) represents the cost of producing the 2001th unit of product.
Explanation:
The complete question
Consider the following cost functions.
a. Find the average cost and marginal cost functions.
b. Determine the average and marginal cost when x=a.
c. Interpret the values obtained in part (b).
C(x)=1000+0.1x, 0≤x≤5000, a=2000
Solution
a) The average cost is given as the total cost divided by the quantity produced.
A(x) = C(x) ÷ x
C(x) = 1000 + 0.1x
A(x) = (1000 + 0.1x) ÷ x = (1000/x) + 0.1
A(x) = 0.1 + (1000/x)
The marginal cost is given as the first derivative of the cost function with respect to the quantity of products produced.
M(x) = (dC/dx)
C(x) = 1000 + 0.1x
M(x) = (d/dx) (1000 + 0.1x) = 0.1
b) To calculate these values at x = a = 2000
Average cost at x = 2000
A(x) = 0.1 + (1000/x) = 0.1 + (1000/2000) = 0.1 + 0.5 = 0.6
Marginal Cost at x = 2000
M(x) = 0.1
c) The average cost is the cost per unit of producing a particular quantity of product.
The marginal cost is the cost of producing an extra unit of product.
Hence, the average cost calculate at x = 2000 in (b) represents the average cost of producing the first 2000 units of product and the marginal cost calculated at x = 2000 in (b) represents the cost of producing the 2001th unit of product.
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