When competition increases do prices increase?

No, this is not true! Competition has an inverse relationship with price. As competition increases, prices tend to decrease because competitors try to capture a bigger market share by decreasing product prices.

On the other hand, demand has a direct relationship with price. That is, when demand increases, prices tend to increase. The reason is the limited availability of that high-demand product. In the short-term, supply cannot be increased to meet the increased demand, so the product's price is increased to reduce the customers' affordability and ultimately balance the demand.