There's no single definitive answer to the average price of a car in 1981. The average price varied greatly depending on the type of car (domestic vs. import, size, features), the source of the data (manufacturer reported vs. consumer surveys), and how the average was calculated (mean vs. median).
However, various sources suggest the average new car price in the United States in 1981 was in the range of $7,000 to $8,000. Keep in mind this is a rough estimate and the actual average could have been slightly higher or lower.