To determine the new average tax rate that will result in a 13.5% increase in tax revenues, we need to calculate the initial tax revenue and then find the new tax rate that will achieve the increased revenue.

Here's a step-by-step breakdown of the solution:

1. Calculate the initial tax revenue:

   The initial tax revenue is determined by multiplying the average income by the average tax rate.

   $\text{Initial Tax Revenue} = \text{Average Income} \times \text{Initial Tax Rate} = 64,000 \times 0.20 = 12,800$

2. Determine the target tax revenue after a 13.5% increase:

   A 13.5% increase in tax revenue can be calculated as:

   $\text{Target Tax Revenue} = \text{Initial Tax Revenue} \times (1 + 0.135) = 12,800 \times 1.135 = 14,528$

3. Find the new tax rate that will achieve the target revenue:

   To find the new average tax rate, we set up the equation using the target tax revenue and solve for the new tax rate:

   $\text{New Tax Rate} = \frac{\text{Target Tax Revenue}}{\text{Average Income}} = \frac{14,528}{64,000}$

Let's calculate this new tax rate:

$\text{New Tax Rate} = \frac{14,528}{64,000} \approx 0.227$

So, the new average tax rate is approximately 22.7%.

This new tax rate will result in a 13.5% increase in tax revenues, assuming the income effect applies uniformly across all taxpayers.

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Would you like further details, or do you have any other questions?

Here are some related questions you might find interesting:

1. How would the result change if the average income were different?
2. What is the income effect, and how does it impact tax revenue calculations?
3. How would changes in taxpayer behavior affect this tax rate increase?
4. What would be the impact of different tax rates on various income groups?
5. How does the marginal tax rate differ from the average tax rate, and why is this important in tax policy?

Tip: Always consider how changes in tax policy might affect taxpayer behavior, as this can impact the expected revenue differently than projected purely by arithmetic adjustments.