Each dollar of retained earnings is translated into at least one dollar of market
Not quite, retained earnings is profits from the business less any dividends paid out to shareholders, and its a component of "shareholder equity" in the balance sheet. So if a company makes $100 in total profit and pays out $20 in dividends, retained earnings would be $80.
Market value is the market cap of the company. So if the company has increased retained earnings by $80 a year you want the market cap (share price times total number of issued shares) to increase by at least $80 if not more. It is a measurement of whether or not the company's share price is keeping up with the growth of the company's earnings, and the amount by which it increases over the amount of retained earnings will reflect that company's return on equity over and above the cost of capital.
In other words, do not buy companies whose share price is declining over the long term, as this indicates a poor return on retained earnings.