Question

Assuming the marginal cost curve is a smooth J-shaped curve, the corresponding total cost curve has a (an) a. linear shape. b. S-shape. c. U-shape. d. reverse S-shape.

Short answer

The correct answer is (c) U-shape. Based on the given information of a smooth J-shaped marginal cost curve, the corresponding total cost curve would initially increase at a decreasing rate and then increase at an increasing rate, resulting in a U-shaped curve.

Step-by-step solution

Review the given information

We are given that the marginal cost curve is a smooth J-shaped curve. This means that the marginal cost initially decreases as output increases and then starts to increase at a certain point. Now we will analyze the options provided for the shape of the total cost curve.

Analyze the options

We have four options to look at: a. Linear shape: This means that the total cost curve would be a straight line, increasing at a constant rate. This is not consistent with a J-shaped marginal cost curve. b. S-shape: An S-shaped total cost curve would imply that the total cost initially increases at a decreasing rate, then increases at an increasing rate, and finally increases at a decreasing rate again. This does not align with a J-shaped marginal cost curve. c. U-shape: A U-shaped total cost curve would imply that the total cost initially increases at a decreasing rate and then increases at an increasing rate. This is consistent with a J-shaped marginal cost curve, as the marginal cost curve is the derivative of the total cost curve. d. Reverse S-shape: A reverse S-shaped total cost curve would imply that the total cost initially increases at an increasing rate, then increases at a decreasing rate, and finally increases at an increasing rate again. This does not align with a J-shaped marginal cost curve.

Conclusion

Based on the analysis of the options, we can conclude that if the marginal cost curve is a smooth J-shaped curve, the corresponding total cost curve has a U-shape. Therefore, the correct answer is (c) U-shape.

Key concepts

Marginal Cost Curve

Understanding the marginal cost curve is fundamental in economics as it reveals how the cost of producing one additional unit changes with the level of production. Imagine a company that makes handmade guitars. Initially, as they start producing more guitars, they become more efficient, and the cost per guitar goes down since workers become more skilled and the company can buy materials in bulk. This decreasing marginal cost is represented as the downward-sloping part of the marginal cost curve.

However, there comes a point where producing more guitars will involve hiring more workers, possibly at a higher cost, or working overtime, which will increase the cost of production for each additional guitar made. This is when the marginal cost starts to rise, leading to the upward-sloping portion of the J-shaped marginal cost curve. Thus, the curve reflects increasing costs after a certain output level, signifying the law of diminishing returns where the efficiency gains decrease with the increase in production.

Total Cost Curve

The total cost curve gives us a broader view of production costs by summing up all costs (both fixed and variable) for different levels of output. If we consider the guitar company example, initially, as more guitars are produced, the total cost will rise at a decreasing rate because the average cost per guitar is falling (thanks to efficiencies). As production continues to increase, the company might need to outlay more for labor, materials, and possibly extend their facilities.

These increased costs cause the total cost to start rising at an increasing rate, shaping the total cost curve into a U-like form. In essence, the total cost curve first flattens out because of initial economies of scale and then starts to rise steeply as the effects of diseconomies of scale set in. This visual representation helps businesses determine the optimal production level to minimize costs.

J-shaped Curve

A J-shaped curve is a graphical illustration that describes certain economic behaviors. For instance, in the context of the marginal cost, it begins with a downward slope reflecting the initial decrease in the marginal cost with increased production. This is indicative of gaining efficiencies, such as buying raw materials in bulk or improving labor proficiency.

However, the curve eventually bends upward, marking the point where increased production leads to higher marginal costs, thus forming the shape of the letter 'J'. This is where the concept of the law of diminishing marginal returns kicks in, meaning that adding more of a single factor of production, while keeping others constant, will eventually produce lower incremental per-unit returns.

U-shaped Curve

The U-shaped curve is often seen in the context of the total cost curve in economics. It begins with a gentle slope downwards as production starts, representing economies of scale where the cost per unit decreases as the quantity increases. As the firm continues to produce more, however, it eventually encounters diseconomies of scale—where the cost per additional unit begins to increase.

This results in the total cost rising at a faster rate, creating the upward slope of the 'U'. Understanding when the curve starts to turn upwards is crucial for businesses as it indicates the threshold beyond which increasing production is no longer cost-effective, guiding decisions on what level of output maximizes profit.