Preheat oven to 400 degrees F (200 degrees C). Lightly grease a cookie sheet.
In a large bowl, cream together butter and 1 cup sugar. Blend in eggs. In a medium bowl, sift together flour and baking soda; gradually beat into butter mixture, alternating with 1/2 cup lemonade concentrate. Drop mixture by rounded teaspoons onto the prepared cookie sheet.
Bake 8 to 10 minutes in the preheated oven, until lightly brown. Brush lightly with remaining lemonade, and sprinkle with remaining sugar.