Question

The short-run cost function of a company is given by the equation tc= 300 65q, where tc is the total cost and q is the total quantity of output, both measured in thousands.

a. what is the company’s fixed cost?
b. if the company produced 100 thousand units of goods, what would be its average variable cost?
c. if the company produced 100 thousand units of goods, what would be its marginal cost of production?
d. if the company produced 100 thousand units of goods, what would be its average fixed cost?
e. suppose the company borrows money and expands its factory. its fixed cost rises by $50,000, but its variable cost falls to $45,000 per 1000 units. the cost of interest (i) also enters into the equation. each 1-point increase in the interest rate raises costs by $3000. write the new cost equation.

Answer 1

a. The company's fixed cost is $300,000. b. The average variable cost when producing 100 thousand units of goods is $65,000. c. The marginal cost of production when producing 100 thousand units of goods is $65,000.

Step-by-step explanation:

a. The fixed cost can be determined by looking at the equation for total cost (tc). In this case, the fixed cost is the constant term (300) in the equation, so the company's fixed cost is $300,000.

b. To find the average variable cost, we divide the variable cost by the total quantity of output. In this case, the variable cost is 65q, so when q=100, the average variable cost is (65*100) / 100 = $65,000.

c. The marginal cost of production is the change in total cost when producing one additional unit of output. In this case, the change in total cost is equal to the change in variable cost, which is 65. Therefore, the marginal cost of production when producing 100 thousand units of goods is $65,000.

d. To find the average fixed cost, divide the fixed cost by the total quantity of output. In this case, the fixed cost is $300,000 and the total quantity of output is 100 thousand units, so the average fixed cost is $300,000 / 100 = $3,000 per unit.

e. The new cost equation can be written as tc = (300 + 50q) + (45q + 3000i), where q is the total quantity of output and i is the interest rate.