Who determines the market value of a property?
On a refinance, lenders will use the appraised value for calculating the loan-to-value ratio for the new mortgage loan. So in that case, the appraiser determines the value.
For a purchase, the property seller sets the price, along with the real estate agent who will assist the seller in establishing the price. They perform a Comparative Market Analysis (CMA), which real estate agents in most states are allowed to perform without an Appraiser's License or Certification. The CMA is vital to the agent’s preparation for a listing, examining recent property sales in the neighborhood to arrive at a listing price. Typically the agent will suggest a price to the seller based on the CMA though the seller may choose to list their property for a higher price. However, again, lenders will use the appraised value for calculating the loan-to-value ratio for the buyer's new mortgage.