Answer: to consider 14 years into the future "There will be a rightward shift of the supply curve for babysitting services 14 years from now, which will result in a higher equilibrium price and a higher equilibrium quantity". Which means option "A" is most correct.
Explanation: We shall Analyse the scenario in steps for your easy understanding and clarification.
STEP 1: In 14 years time the babies born during the child birth rate increase will start giving birth, and the babies born today will become they babysitter.
STEP 2: babies born three years ago are twice babies born today.
STEP3: The twice rate of babies born three years ago will want the normal rate of babies born today to serve them as babysitter.
STEP 4: In 14 years time, the parents that will need the service of baby sitters will be twice the available babysitter, because the parent in 14 years time are the ones born during the child birthrates increase. And the babysitter will be the one born today, during the normal child birth rate.
Form the analysis in the steps we can see that, they will be an increase in the demand of babysitter in 14 years time, which may lead to increase in price, Therefore, they will be an increase in the quantity of services needed.
There will be a rightward shift of the supply curve, because the curve will start from babysitting service when demand was normal to when demand comes high and then back to normal.
NOTE: The quantity in this scenario is not the quantity of babysitter available, but the quantity of parents in need of babysitter service.
THEREFORE FOR BABY SITTERS SERVICES, AS THE EQUILIBRIUM QUANTITY INCREASE, THE EQUILIBRIUM PRICE INCREASE TOO.