Cost Functions and Marginal Analysis

The video tutorial explains the cost function C(Q) = 20.5Q + 84,000, used to calculate the total cost of producing Q units. It demonstrates how to find the total cost for 800 units and the marginal cost of the 801st item. The tutorial highlights the linear nature of the cost function, where the cost increases by $20.50 for each additional unit. It also discusses using derivatives to approximate marginal cost, emphasizing that the derivative of the cost function provides a consistent marginal cost value.

What is the formula for the total cost function given in the video?

• C(Q) = 25Q + 80,000

• C(Q) = 30Q + 70,000

• C(Q) = 20.5Q + 84,000

• C(Q) = 15Q + 90,000

How much does it cost to produce 800 units according to the cost function?

• $90,000

• $100,400

• $110,000

• $120,500

What is the cost of producing the 801st item?

• $25.00

• $15.00

• $20.50

• $30.50

What is the term used to describe the cost of producing one additional unit?

• Marginal Cost

• Variable Cost

• Fixed Cost

• Average Cost

What is the slope of the linear cost function?

• 30

• 25

• 20.5

• 15

How does the cost change as Q increases by 1 unit?

• Increases by $25.00

• Increases by $20.50

• Increases by $15.00

• Increases by $30.50

What is the derivative of the cost function C(Q) = 20.5Q + 84,000?

• 15

• 20.5

• 25

• 30

What does the derivative of the cost function represent in this context?

• Average Cost

• Fixed Cost

• Total Cost

• Marginal Cost

Why might the derivative of the total cost function be used?

• To find total revenue

• To approximate marginal cost

• To determine average cost

• To calculate fixed costs

What is the constant term in the cost function C(Q) = 20.5Q + 84,000?

• 20.5

• 0

• Q

• 84,000