If dividends are taxed at a lower rate than capital gains, which of the following statements best caputres the relation between dividends and stock price change on ex$-$dividend day?

Stock price should increase by an amount more than the dividend amount

Stock price should increase by an amount less than the dividend amount

Stock price should decrease by an amount less than the dividend amount

Stock price should decrease by an amount more than the dividend amount

There is no relation between taxes and ex$-$dividend day price behavior