A new technology is announced which allows manufacturers to produce widgets for less. Widgets are a key input in the production of whatchamacallits. What would we expect to happen to the market for whatchamacallits?

The supply curve will shift to the right.

Explanation:

Whenever there is increase in supply of goods, due to any reasons the supply curve moves to right.

Here, as with the introduction of new technology, the cost of widgets one of the key inputs to the production of whatchamacallits, is reduced,

Accordingly, with the reduction in price of inputs the cost for manufacturers will decrease and they will produce more.

As a result the supply for the product whatchamacallits will increase, and with that the supply curve will move right.