MATEMATICAL ECONOMICS S1 BISNIS DIGITAL UNIVERSITAS GARUT

Summary

In this video, Diana Unisa, a student from the Digital Business program at Garut University, explains the concept of marginal cost. She introduces the total cost function and shows how to calculate marginal cost through its derivative. Using an example, she walks through the calculation of total cost for producing one unit of a product and marginal cost for producing the second unit. The video offers a clear, step-by-step explanation of these fundamental concepts in business economics.

Takeaways

• 😀 The speaker introduces themselves and their academic details (name, student ID, course, and university).
• 😀 The topic of the presentation is 'Marginal Cost' (biaya marginal), a key concept in economics.
• 😀 Marginal cost refers to the additional cost incurred when producing one more unit of a product.
• 😀 The speaker explains that marginal cost can be mathematically derived by taking the first derivative of the total cost function.
• 😀 The total cost (TC) function is given by: TC = q^3 - 3q^2 + 4q + 4, where q represents the quantity produced.
• 😀 The first step is to calculate the total cost for producing 1 unit (Q = 1).
• 😀 Substituting Q = 1 into the TC function yields a total cost of 1.
• 😀 The marginal cost function is the derivative of the total cost function: MC = 3q^2 - 6q + 4.
• 😀 To calculate the marginal cost when producing the second unit (Q = 2), the speaker substitutes Q = 2 into the MC function.
• 😀 The result for the marginal cost of the second unit is 4, meaning the cost of producing the second unit is 4.
• 😀 The speaker concludes by summarizing the steps and apologizing for any mistakes, before thanking the audience.

Q & A

What is Marginal Cost?

Marginal Cost is the additional cost required to produce one more unit of a product.

How is Marginal Cost calculated in mathematics?

Marginal Cost can be calculated by taking the first derivative (or 'derivative') of the Total Cost (TC) function, which is typically expressed as a function of the quantity produced (Q).

What is the given Total Cost (TC) function in the problem?

The given Total Cost (TC) function is TC = q^3 - 3q^2 + 4q + 4.

What does TC represent in the problem?

TC represents the Total Cost, which is the overall cost of producing a certain quantity of products.

How do we find the Marginal Cost from the Total Cost function?

To find the Marginal Cost, we take the first derivative of the Total Cost function. For the given TC function, the derivative is TC' = 3q^2 - 6q + 4.

What is the Total Cost for producing 1 unit of product?

The Total Cost for producing 1 unit of product is calculated by substituting Q = 1 into the TC function, resulting in TC = 1.

What is the Marginal Cost when producing the second unit of product?

The Marginal Cost when producing the second unit is calculated by substituting Q = 2 into the Marginal Cost function (TC'), resulting in a value of 4.

Why is the derivative of a constant term equal to 0 in the given TC function?

The derivative of a constant term is 0 because in calculus, the rate of change of a constant value does not change with respect to the quantity produced.

What does the function TC' = 3q^2 - 6q + 4 represent?

The function TC' = 3q^2 - 6q + 4 represents the Marginal Cost, or the additional cost incurred when producing one more unit of product.

What is the significance of the value of Marginal Cost for the second unit of production?

The Marginal Cost of 4 for the second unit indicates that it costs an additional 4 currency units to produce the second product.