How does technological progress affect the firms' supply curve?

The correct option is Shift to the right.

Here is the step-by-step explanation of why technological progress shifts a firm's supply curve to the right:

1. Understanding the Supply Curve:
A firm's supply curve represents the relationship between the price of a good and the quantity that the firm is willing and able to supply, holding other factors constant. The supply curve is typically upward-sloping, reflecting that higher prices incentivize higher production. Under perfect competition, a firm's supply curve is determined by its marginal cost ($\mathrm{MC}$) curve above the minimum average variable cost.

2. The Impact of Technological Progress:
Technological progress implies an improvement in the art of production or the introduction of more efficient machinery, techniques, or organizational methods. This advancement allows the firm to produce the same level of output using fewer inputs, or produce a greater level of output using the same quantity of inputs.

3. Reduction in Production Costs:
Because inputs are used more efficiently, the cost of producing each additional unit of output decreases. Mathematically, this means that both the average cost ($\mathrm{AC}$) and the marginal cost ($\mathrm{MC}$) of production decrease at every level of output.

4. Graphic Representation of the Shift:
When marginal costs decrease, the marginal cost curve shifts downward (or outward to the right). Since the supply curve is derived directly from the marginal cost curve, a reduction in marginal cost means that at any given price level, the firm can now profitably produce and offer a larger quantity of the good for sale. This increase in supply is represented graphically as a rightward shift of the entire supply curve.