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The real post-tax consumption wage, denoted by $w$, represents a worker's actual purchasing power after taxes. It is calculated by dividing the nominal take-home wage ($W$) by the consumer price level ($P_c$). The formula is: $w = W/P_c$. This variable is the key measure of wages used when adapting the WS-PS model for tax analysis.

Definition of Real Post-Tax Consumption Wage ($w$)

Given the scenario below, calculate the worker's real post-tax consumption wage ($w$) and briefly explain what this value signifies about their economic situation.

Calculating and Interpreting Purchasing Power

A worker's nominal take-home wage ($W$) increases by 3% in one year. For their real post-tax consumption wage ($w$) to have remained exactly the same, what specific change must have occurred in the consumer price level ($P_c$)? Explain your reasoning by describing the relationship between these three variables.

Analyzing Wage and Price Level Changes

If a worker's nominal take-home pay (the amount received after income taxes) increases by 5% in a given year, their real purchasing power, as measured by the post-tax consumption wage, must also increase.

A government increases the national sales tax, which is applied to most goods and services. Assuming a worker's nominal take-home pay (the amount they receive after income taxes are deducted) does not change, what is the direct and immediate impact on the components that determine their real post-tax consumption wage ($w$)?

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