When oil industry slump hits home

''If you have 18 percent unemployment in Detroit and under six here,'' says the mayor of Louisiana's fastest growing city, ''obviously on a comparison basis , we're not badly off.''

But Mayor ''Dud'' Lastrapes and most people here only compare Lafayette with its own boom town past. Along with creating at least a thousand local millionaires, Lafayette's role as a major offshore oil industry center pushed the parish from 1970's ninth place into top rank in per capita income for Louisiana in 1980. Fred Cole from Arkansas was one of thousands who moved here to cash in on the boom. Now the crude oil buyer spends a lot of time sitting in his office in Lafayette's sprawling Oil Center, home to more than 400 oil companies.

''This industry is just kind of stalled,'' Sunoco's Mr. Cole explains. ''People are either not drilling or else shutting in their wells and not producing because demand is down and prices are so low.''

At least temporarily, Lafayette's boom is over. The mayor counts the costs: new construction down sharply and sales tax revenue cut to a 15 percent annual rate of increase rather than the ''normal'' 24 percent. ''The big problem now is keeping up with growth,'' Lastrapes explains. With revenue down sharply and $ 500 million needed for new bridges, underpasses, drainage projects, and a police and fire training center, the mayor is waiting for ''another boom with natural gas price decontrol, as we had with oil deregulation.''

Lastrapes is confident Lafayette will pull out of its slump. ''It all depends on the activity generated by the oil industry,'' he admitted, but added with a grin that better times are coming because ''the need for energy is still around.''