The Board of Directors would like you to undertake the following tasks:

1. Taxes can have drastic impacts on consumer and producer welfare by shifting the market closer to the left, decreasing consumer and producer surplus. This process, however, can be costly to the economy due to the Dead Weight Loss (DWL) - the inefficiency generated by the distortion of the allocation of resources in the economy due to taxes. As illustrated in the diagram above, taxes result in decreased areas of consumer and producer surplus. This means that the government gains an increase in revenue. This can be expressed graphically as a shift in the demand curve and the dead weight loss due to the inefficiency of the transfer of resources can be understood by the triangle area redistributed from the previous consumer and producer welfare.

2. In the macroeconomy, taxes can have a similar effect on the AD-AS model. This model is composed of the aggregate supply and aggregate demand curves, which represent the combination of goods and services at a given price in an economy. Tax increases can lead to an increase on the costs of businesses, resulting in a decrease in production. Graphically, this would mean a shift of the AS curve to the left and the AD-AS intersection would shift to the left as well. This would result in a decrease in consumption and output, an increase in prices and, in most cases, an increase in unemployment.

3. In an AD-AS model, an increase in taxes that improve people's health could have potential long-term benefits for the economy. This is due to the idea that increased productivity in the labor force as a result of improved health can have positive impacts on economic growth in the long-run. Despite the fact that a tax increase would lead to a decrease in the quantity demanded and the AD-AS curves would shift to the left, the long-term benefits of improved health could outweigh the costs, leading to a net increase in economic output over time.

4. An empirical econometric model could be used to assess the health and economic growth consequences of a 'fat tax'. This model could combine quantitative data on the health outcomes of a fat tax with economic features, such as changes in GDP, local employment, prices, and consumer surplus. This type of analysis could accurately reflect the impact of such a policy and help policymakers inform their decisions and determine the potential macroeconomic effects of introducing such as tax.