Beat 1/2 cup butter in a mixing bowl with an electric mixer for 30 seconds. Add granulated sugar, baking powder, and baking soda; beat until combined. Beat in egg and 1/3 cup lemonade concentrate. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour with a wooden spoon, If desired, add red food coloring to tint dough pink.
Drop by rounded teaspoons 2 inches apart on an ungreased cookie sheet. Bake in a 350 degree F oven for 10 to 12 minutes or until edges are golden. Cool on cookie sheets for 1 minute; transfer cookies to wire racks and cool completely. For frosting, beat together 2 tablespoons butter, powdered sugar, and 2 teaspoons lemonade concentrate and enough water (3 to 4 teaspoons) to make of spreading consistency. If desired, add red food coloring to tint the frosting a delicate pink. Frost cookies. Makes 36.