Explanation:

The U-shaped average cost curve is a graphical representation of the relationship between the average cost per unit of output and the quantity of output produced. The curve is called U-shaped because it has a downward slope at low levels of output, reaches a minimum point, and then has an upward slope as output increases.

The U-shaped average cost curve is based on the law of variable proportions, also known as the law of diminishing marginal returns. This law states that as additional units of a variable input are added to a fixed input, the marginal product of the variable input will eventually decrease.

The U-shaped average cost curve is based on this law because when the marginal product of the variable input is increasing, the average cost per unit of output is decreasing. However, when the marginal product of the variable input starts to decrease, the average cost per unit of output starts to increase.

The U-shaped average cost curve is not based on the law of increasing cost, which states that as the production of one good increases, the opportunity cost of producing another good increases. Nor is it based on the law of decreasing cost, which states that as the production of one good increases, the opportunity cost of producing another good decreases. Finally, it is not based on the law of constant returns to scale, which states that as all inputs are increased by a certain proportion, output will increase by the same proportion.

Therefore, the correct answer is option 'D', which states that the U-shaped average cost curve is based on the law of variable proportions.