If a new product is being introduced into the Market, is it appropriate for the price to be high whilst competitors prices are low?

It will all depend on your core marketing strategy. People buy products on benefits and advantages, price comes later. Yes if you want to give a tough competition to others you have to design a clever pricing strategy. 

this is a complicated question with many parameters to consider. The information given in the question is insufficient for an educated answer. You will need to concider paramaters such as : the competition itself, product quality, Distribution, awareness of brand, too name but a few..SWOT and PEST analysis of the market is essential to answer the question.

Pricing policy varies depending on several factors: market demand, competitors, your own reputation, quality, your customers, added value, ,....

A business must have a set of questions to be answered by business itself based on "IFs & BUTs" since this strategy involves great risk of failure. the business should have a good contingency plan.