with the level of government spending given, why might an increase in the tax rate cause an increase in the budget deficit?

Here is a link to an explanation of the Laffer curve. Google Laffer Curve for more info.

http://en.wikipedia.org/wiki/Laffer_curve

An increase in the tax rate can potentially cause an increase in the budget deficit due to several factors:

1. Tax Elasticity: When tax rates are increased, it may lead to a decrease in overall tax revenue collected if the tax base is responsive or elastic. For example, if people find the higher tax rate burdensome, they may engage in tax avoidance strategies such as reducing taxable income, shifting investments to tax-exempt assets, or taking advantage of tax loopholes. This can result in a decrease in tax revenue collected and contribute to a higher budget deficit.

2. Economic Impact: Increasing tax rates can also have an impact on economic activity. Higher taxes may reduce disposable income and decrease consumer spending, leading to a slowdown in economic growth. This, in turn, can lead to a decrease in tax revenue collected from other sources such as sales taxes or corporate taxes. If the decrease in tax revenue outweighs the additional revenue generated by higher tax rates, it can contribute to a higher budget deficit.

3. Laffer Curve Effect: The Laffer curve theory suggests that there is an optimal tax rate that maximizes tax revenue for the government. If tax rates are already on the right side of the Laffer curve, meaning tax rates are too high, increasing them further may actually result in a decrease in tax revenue. This is because higher tax rates can discourage work, investment, and entrepreneurship, leading to lower taxable income and revenue. If the decrease in revenue outweighs the additional revenue from higher tax rates, it can lead to a larger budget deficit.

To accurately determine the impact of an increase in the tax rate on the budget deficit, a detailed analysis of the specific tax system, taxpayer behavior, economic conditions, and revenue projections is essential. This analysis is typically conducted by economists, tax policy experts, and government agencies that specialize in public finance.