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Please explain why the short-term average cost curve and short-term marginal cost curve are both U-shaped.
Because they are all determined by the law of diminishing marginal returns.

Because this law is at work, with the increase of variable factors, the marginal product will increase first and then decrease, so the marginal cost will decrease first and then increase, and the result is that the marginal cost curve must be U-shaped.

This law also determines that the average output will increase first and then decrease, so that the average cost will decrease first and then increase, so it is also U-shaped.

The relationship between the two curves is: when the AC curve is inclined downward, the MC curve is below the AC curve; When the AC curve inclines upward, the MC curve must be above the AC curve; They intersect at the lowest point of the AC curve.

Short-term cost curve:

The short-term cost curve is also called the "operating curve". Graphical representation of related cost function under different output when several production factors remain unchanged or cannot be adjusted.

This paper mainly explains the basic relationship between cost and output under a certain production scale, which is used for the recent business decision of enterprises. The traditional short-term cost curve is shown in the following figure. In the figure, TVC is the total variable cost, TFC is the total fixed cost, TC is the total cost, AFC is the average fixed cost, AVC is the average variable cost, ATC is the average total cost, and MC is the marginal cost.

Marginal cost:

In economics and finance, marginal cost refers to the increment of total cost per unit of newly produced products (or purchased products). This concept shows that the cost per unit product is related to the total product.

For example, the cost of producing only one car is extremely huge, while the cost of producing 10 1 is much lower, and the cost of producing 10000 is even lower (this is because of the benefits brought by economies of scale).

But considering the opportunity cost, with the increase of output, the opportunity cost may also increase. Again, the materials used in the production of a new car may be more useful, so we should try to produce as many cars as possible with the least materials and improve the marginal income. Marginal cost is abbreviated as MC or MPC.

Reference link: Baidu Encyclopedia: Short-term cost curve

Baidu Encyclopedia: Marginal Cost