When you go to a restaurant you're paying for a service of the chefs cooking the food for you and preparing it for you.
So the Pasta you order at the restaurant has to be more expensive than the pasta you would make at home so they can pay the overhead costs of the restaurant and the chefs and for them to profit.
There's really not much difference in the pasta you make at home and the pasta you order in a restaurant but then again maybe some restaurants use a few more ingredients but still they have to charge more for the pasta to make a profit and to pay their employees.
At home you're not using chefs to make the pasta or paying employees and you're not looking to make a profit so that's why the pasta is more expensive in a restaurant than it is at home.