Statement : 

The government has increased taxes on cigarettes to reduce smoking rates.

Assumptions :

 I. Increasing taxes is an effective way to reduce smoking rates.

II. People will stop smoking altogether due to increased taxes.

Given statement: 

The government has increased taxes on cigarettes to reduce smoking rates.

Assumptions: 

I. Increasing taxes is an effective way to reduce smoking rates. → Implicit

The government takes this action (increasing taxes) with the specific goal of reducing smoking rates. For them to implement this measure with this objective, it must be assumed that they believe this action will be effective in achieving that reduction.

II. People will stop smoking altogether due to increased taxes. → Not Implicit

The statement indicates a goal to "reduce smoking rates," which implies a decrease in smoking, not necessarily a complete cessation by all smokers. This assumption goes beyond the stated intention.

Thus, Only assumption I is implicit.

Hence, "Option 1" is the correct answer.