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Suppose competition increased, which increased elasticity of demand from -2 to -3

Economics

Suppose competition increased, which increased elasticity of demand from -2 to -3. Your current price for your product is $10. If demand elasticity is -3, how much should you now charge?

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Recall that the relationship between the marginal revenue and the price elasticity of demand as:

If the current elasticity of demand is and the firm is charging a price equal to, then the firm's marginal revenue is:

Assuming that the firm is already optimizing its profits (producing where MR=MC), then if the elasticity becomes , the price that the firm should charge is now equal to: