# Why does average variable cost = marginal cost for this function?

I was hoping someone could explain the following. Suppose the short-run total cost function is TC = 50 + 12Q. Which of the following statements is true at all levels of production?

The correct answer given was that MC = AVC

Could someone explain to me why please?

• Do you know how to derive MC and AVC in general? – Herr K. Nov 2 '19 at 20:27
• MC = derivative of TC and AVC is TVC/Q? – Andrew Andreas Nov 2 '19 at 22:10

So using your above statements in the comments it should be relatively clear how to find that $$MC = AVC$$. $$MC = \frac{\partial TC}{\partial Q} = 12$$ and then using the fact that variable cost is $$12Q$$ $$AVC = \frac{VC}{Q} = 12$$
• Basically, given the functional form for the total cost function, you can see that neither of the above depend on $Q$. The marginal cost is constant and does not vary at different points. You can think of it in terms of the graph, if you were to plot your total cost function it would be an upward sloping line starting at 50 with a slope of 12. And if marginal cost is the derivative then it is the slope, which does not change. Same thing for average variable cost, it does not vary with $Q$. And this makes sense as the variable cost is $\$12$per unit of$Q\$, which does not change. – Brennan Nov 3 '19 at 17:25