Can someone explain what is a cubic cost function? I'm taking a managerial economics course, but I've never taken any algebra or calculus; so I'm struggling. I'd like to grasp the purpose of what it is and then try to figure out how to do it. thanks!
A so-called cubic function is nothing else than a polynomial function of degree 3.
f(x)=ax^3+bx^2+cx+d, where a,b,c,d are fixed, but not determined constant coefficients, imposed the condition a != 0.
Wow, this definition is like greek. What is a polynomial function of degree 3? I know what a constant is and also a coefficent. But what is "imposed the condition a!=0? Can someone explain this in a simpler way that doesn't involve algebra or calculus? Thanks
Basically, the point of cubic is that you can use the cube (third power) of the number of things produced to predict the total cost of making that many things. It so happens that x^3 (x cubed) very nicely represents certain economies/not of scale in production; it "looks right".
So the whole point is that some algebra can provide a nice formula that approximates the reality of cost functions for which marginal cost (the cost of "making one more") first goes down, then goes up. And some calculus can confirm it.
Of course! I'll explain what a cubic cost function is and how to understand it intuitively without prior knowledge of algebra or calculus.
In managerial economics, a cost function represents the relationship between the quantity of production and the cost associated with producing that quantity. A cubic cost function is a specific type of cost function where the cost is a cubic function of the quantity of production.
To understand a cubic cost function, let's begin with a simpler example: a linear cost function. In a linear cost function, the cost increases at a constant rate as the quantity of production increases. For instance, if it costs $10 to produce 1 unit, then it would cost $20 to produce 2 units, $30 for 3 units, and so on.
A cubic cost function is different because the cost does not increase at a constant rate. Instead, it increases at an accelerating rate. This means that the cost increases exponentially as the quantity of production increases. For example, if the cubic cost function is C(q) = q^3, where q represents the quantity of production, then the cost would be:
- C(1) = 1^3 = 1
- C(2) = 2^3 = 8
- C(3) = 3^3 = 27
- C(4) = 4^3 = 64
- C(5) = 5^3 = 125
As you can see, the cost increases significantly with each additional unit produced, which is why it is called a cubic cost function.
Now, to determine the specific cubic cost function in real-world situations, knowledge of algebra or calculus would be necessary. These mathematical tools can help you estimate the exact equation for a cubic cost function based on historical cost and production data. Nevertheless, it is still beneficial to understand the concept and intuition behind a cubic cost function to make informed decisions in managerial economics.
I hope this explanation helps you grasp the purpose of a cubic cost function without delving into the mathematical details. Good luck with your course!