Final answer:
When the customer pays the previously written-off balance, Barnes Books experiences an increase in assets due to the receipt of cash and no change in liabilities.
Step-by-step explanation:
When Barnes Books writes off a bad debt of $7,000, it reduces both its accounts receivable (asset) and the allowance for doubtful accounts (contra-asset). The net effect on total assets is zero. However, when the customer unexpectedly pays the $7,000 balance, Barnes Books records an increase in cash (asset) and reverses the previous write-off by increasing accounts receivable and decreasing the allowance for doubtful accounts. The end result is an increase in assets due to the cash received and no change in liabilities. Therefore, the option that correctly reflects the effect of this transaction on the financial statements of Barnes Books is 1) Increase in assets and decrease in liabilities (although the decrease here is in a contra-asset account, not a true liability).