Quantify the costs/benefits to the company of buying you a second monitor. How much more productive does it make you? Can you quantify the benefits somehow, either as increases to the bottom line, or recouping lost opportunities? (You might not be paid by the hour, so labor costs may vary - think situations where your higher productivity could save the company money.) Formulate a logical argument. Write a short business case - one or two pages long. Not too long - you just want to make your case, not be pedantic or boring.(Google how to write a business case.) If you can make your case, and your boss/company is somewhat rational, you should have your monitor. Good Luck!