The governor of a central province told employers to contribute to a Kremlin campaign to boost the birthrate by giving couples the day off to have sex. And if a woman gives birth in exactly nine months — on Russia’s national day on June 12 — she will qualify for a prize, perhaps even winning a new home. Russia wants to reverse a trend in which the population is shrinking by about 700,000 people a year as births fail to outpace a death rate fueled by AIDS, alcoholism and suicide. This is the third year the Ulyanovsk region, famous as the birthplace of Lenin, has dedicated a day to encouraging couples to produce more babies.