There are differences between the nouns economy and economics, and the adjectives economic and economical.

Nouns:

Economy means a general financial state, eg. The economy has a lot of problems at the moment.

Economics means the financial subject at university, eg. He is studying Economics at the moment.

Adjectives:

Economic means related to the economy, eg. The government needs to revise its economic plans.

Economical means cheap or inexpensive, eg. I bought this detergent because it was more economical.