Assume that due to an increase in demand, the average domestic airline fare increased from $\$ 319.85$ in the fourth quarter of 2013 to $\$ 328.12$ in the first quarter of $2014,$ an increase of $\$ 8.27$. The number of passenger tickets sold in the fourth quarter of 2013 was 151.4 million. Over the same period, the airlines' costs remained roughly the same: the price of jet fuel averaged around $\$ 2$ per gallon in both quarters, and airline pilots' salaries remained roughly the same, averaging $\$ 117,060$ per year in 2013). Can you determine precisely by how much producer surplus has increased as a result of the $\$ 8.27$ increase in the average fare? If you cannot be precise, can you determine whether it will be less than, or more than, a specific amount?