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.

3. Imagine a perfectly competitive firm producing good A with cost function TC=400+20Q-2Q ² +2/3Q ³ , where Q is quantity produced

a. determine the firm’s short run supply curve

b. What is the profit maximizing level of output when price of A is birr 180?

Answer 1

1.Integrating the function:

$Q^3+4Q^2+400Q=100^3+4\times100^2+400\times100=1 080 0000$

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

$TC=\intop60+2.5Q$

$TC=1.25Q^2+60Q$

b. The total cost of 200 units.  

$=1.25(200)^2+60(200)$

$=62,000$

3.a. the firm’s short run supply curve is MC

$MC=TC'=(400+20Q-2Q2+2/3Q3)'=20-4Q+2Q^2$

b.

MC=P

$20-4Q+2Q^2=180$

$20-4Q+2Q^2-180=0$

$2Q^2-4Q-160=0$

$Q^2-2Q-80=0$

Q=10

$profit=MR-MC=180\times10-(20-4\times10+2(10^2))=1800-20+40-200=1620$