Primary productivity is the rate at which energy is converted by photosynthetic and chemosynthetic autotrophs to organic substances. The total amount ofproductivity in a region or system is gross primary productivity.
Secondary production is the generation of biomass of heterotrophic (consumer) organisms in a system. This is driven by the transfer of organic material between trophic levels, and represents the quantity of new tissue created through the use of assimilated food.
Hence,the statement, "The rate of primary productivity is equal to the rate of secondary productivity" , is a FALSE statement.