Economics question: Should each level of output determine a unique cost figure?

Wait what do you mean by unique cost figure?

The question doesn't say anything else besides that. But my understanding is, should each level of output have a different/varied cost of production associated with it?

If you think about the costs - there are fixed and variable costs in the production of a good. So if you want to increase output, your variable costs increase but your fixed costs stay the same.

If a firm exploits economies of scale then it can reduce it long run average costs. In the long run there are only variable costs, no fixed costs, so that means that a reduction in a firm's variable costs per unit.

How about the cost curves? Like for example, marginal costs. In some examples of marginal costs, there comes a point when the marginal costs of an output level stays the same as the one before, and the next output level's MC increases. I hope I explained it well bc I couldn't find an e.g. image on the internet about this although I've seen it all over Econ papers.

Okay so the marginal cost curve is something quite interesting. I'll first give you an example to understand the theory behind the marginal cost curve which explains its shape.
Let's take Domino's - a firm which makes pizzas. In the short run, if the manager of domino's wants to increase output (the number of pizzas dominos makes) he first has to understand that in the short run there is at last one factor of production that is fixed, typically land. This means that he has to increase the number of workers to make more pizzas and increase the output. So let's say he hires more workers for his dominos shop which is a small shop. When he hires more workers, the workers can specialise in part of the pizza production process like one worker focussing on making the sauce, another focussing on taking orders, another putting the toppings on pizzas etc... which increases productivity as more workers an specialise in doing their own part they can become better at it so the marginal cost (the cost of hiring an additional worker or one extra unit input) decreases in the short run because domino's are producing lots of pizzas (lots of output) that the costs can be spread over a larger output so each cost gets smaller. But, then the marginal cost curve as it slopes downwards reaches a point which is called the law of diminishing returns. This law states that it comes a point in time when an additional factor of production produces less output. This is because land (ie the shop) is a fixed factor of production in the short run so this means there is a fixed amount of space for workers so as dominos hires more workers they have less space to move around and they get in the way of each other which just slows the pizza making process down and therefore each worker is less productive and produces less output. This means that the cost per unit input (ie the cost for each worker) increases which explains why the marginal cost curve slopes upwards again
This explain why the marginal cost curve slopes down to show costs decreasing but then reaches a pointand then slopes back up again as firms like Dominos increase output - creating that Nike tick shape for the curve.

Incredible explanation, thank you. I gather that the answer to the original question is yes