Vacancy rates fell and rents went up in Los Angeles County’s office sector during the first quarter. Year over year, vacancy fell to 16 percent from 18 percent during the period, while average rents rose six percent, hitting $2.73 per square foot, according to Cushman & Wakefield. The Westside fared the best during this time frame, while Downtown Los Angeles remained flat. Demand could increase, though. There is only 1.5 million square feet of office under construction right now in the county, which currently has 195.8 million square feet of total inventory.