In response to a cost-reducing technological breakthrough in the production of its product, a profit-maximizing monopolist will normally:

The monopolist will incorporate the breakthrough into their production, but charge the same monopoly pricing for the product.

Explanation:

Because the monopolist is profit-maximizing, they want to both minimize their costs and maximize revenue taken in. Because a breakthrough exists reducing costs, the monopolist will gladly incorporate that into their production function. Because they've monopolized the industry for the product, however, there's no competition to lower the price of the product, and they'll charge the same high price as before since they're a profit maximizing firm.

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