Answer to Question #281856 in Microeconomics for kalehiwot

Question

1. The marginal cost of a trader has been found to be MC = 3Q² +8Q+ 400 . Determine the total variable cost of producing 100 units of the trade’s product.

2. If the fixed cost of manufacturing a product is ETB 10, 000 and the marginal cost at Q units of output is ETB(60+2.5Q). Find:

a. The function for the total cost of manufacturing x units.

b. The total cost of 200 units.

Answer 1

Solution:

1.). Derive Total Variable Cost from the MC:

TVC = ∫ MC dx + k

TVC = ∫ (3Q² +8Q+ 400) dx

= ∫ (Q³ + 4Q² + 400Q)

TVC = Q³ + 4Q² + 400Q

When Q = 100 units

TVC = 100³ + 4(100²) + 400(100) = 1000,000 + 40,000 + 40,000 = 1,080,000

The total variable cost of producing 100 units = 1,080,000

 

2.). a.). Derive the total cost function:

TC = ∫ MC dx + k

K = 10,000

TC = ∫ (60 + 2.5Q) dx + k

TC = ∫ (60Q + 1.25Q²) + 10,000

TC function = 60Q + 1.25Q + 10,000

 

b.). The total cost of 200 units:

Q = 200 units

TC = 60Q + 1.25Q + 10,000 = 60(200) + 1.25(200) + 10,000 = 12,000 + 250 + 10,000 = 22,250

The total cost of 200 units = ETB 22,250