How exactly do you make local prices decrease by making imported goods more expensive? It does not make any sense. If the global market price of a product get artificial higher, one do not lower the local prices. The local prices get increased to match what ever the effective global market price (price + tariff) is.

Of course. The purpose of tariffs is neither to increase nor lower the prices of goods. The purpose of tariffs from the government point of view is to increase self-production, value generating, and self-sustainability. But the practical effect of an tariff is a higher priced product for the consumer. In the word of wikipedia: Typical analyses find that tariffs tend to benefit domestic producers and government at the expense of consumers.