Question

Consider the following Phillips Curve: πₜ=(1−θ) πˉ +θπ t−1​ +(m+z)−αuₜ ​ πˉ =2%,m+z=5%,α=1.67​ In 2022 , the unemployment rate was 3%, and the inflation rate was 6%. You are an employed worker who wants to ask for a raise to keep their purchasing power constant in 2023. What raise (in \%) would you request to your employer if a) Expectations are fully anchored, and the unemployment rate is constant between 2022 and 2023

Answer 1

To keep purchasing power constant in 2023, you would need to ask for a raise of approximately 10%.

Step-by-step explanation:

In this scenario, the student wants to request a raise to keep their purchasing power constant in 2023. To determine the raise percentage, we can use the Phillips Curve equation: πₜ=(1−θ) πˉ +θπ t−1​ +(m+z)−αuₜ.

Since expectations are fully anchored, we can assume πˉ and π t−1 are equal to the actual inflation rate in 2022, which is 6%. We also know that the unemployment rate in 2022 is 3%. By substituting these values into the equation, we can solve for the raise percentage, uₜ.

πₜ=(1−θ) πˉ +θπ t−1​ +(m+z)−αuₜ = (1−θ) πˉ +θπ₀ + (m+z)−αuₜ = (1−θ) π₀ + θπ₀ + (m+z)−αuₜ = π₀ + (m+z)−αuₜ.

Therefore, the raise percentage, uₜ, would be 6% + (5% - 1.67x3%), which equals 9.99%. So, you would request a raise of approximately 10% to keep your purchasing power constant in 2023.

The complete question is:Consider the following Phillips Curve: πₜ=(1−θ) πˉ +θπ t−1​ +(m+z)−αuₜ ​ πˉ =2%,m+z=5%,α=1.67​ In 2022 , the unemployment rate was 3%, and the inflation rate was 6%. You are an employed worker who wants to ask for a raise to keep their purchasing power constant in 2023. What raise (in \%) would you request to your employer if a) Expectations are fully anchored, and the unemployment rate is constant between 2022 and 2023

Answer 2

To keep purchasing power constant in 2023 with fully anchored expectations and a constant unemployment rate, you should request a raise of approximately 5.35%.

Step-by-step explanation:

The Phillips Curve equation provided is:

`\[ \pi_t = (1 - \theta) \bar{\pi} + \theta \pi_(t-1) + (m + z) - \alpha u_t \]`

Where:

-
`\( \pi_t \)` is the inflation rate in period t,

-
`\( \bar{\pi} \)` is the target inflation rate,

-
`\( \theta \)` is the weight on past inflation expectations,

-
`\( \pi_(t-1) \)` is the lagged inflation rate,

- m + z is the exogenous component of inflation,

-
`\( \alpha \)` is the weight on the unemployment rate,

-
`\( u_t \)`is the unemployment rate.

Given
`\( \bar{\pi} = 2\%, m + z = 5\%, \alpha = 1.67\% \)`, and the 2022 values
`\( \pi_(2022) = 6\% \)`
`\( u_(2022) = 3\% \)`, we can substitute these values into the Phillips Curve equation:

`\[ \pi_(2023) = (1 - \theta) * 2\% + \theta * 6\% + 5\% - 1.67 * 3\% \]`

Since expectations are fully anchored (
`\( \theta = 1 \)`) and the unemployment rate is constant
`(\( u_(2023) = u_(2022) = 3\% \))`, we can simplify the equation:

`\[ \pi_(2023) = 2\% + 6\% + 5\% - 1.67 * 3\% = 11\% - 5.01\% = 5.99\% \]`

Therefore, to maintain constant purchasing power, you should request a raise of 5.99% - 0.64% = 5.35% in 2023.

The complete question is: Consider the following Phillips Curve: πₜ=(1−θ) πˉ +θπ t−1​ +(m+z)−αuₜ ​ πˉ =2%,m+z=5%,α=1.67​ In 2022, the unemployment rate was 3%, and the inflation rate was 6%. You are an employed worker who wants to ask for a raise to keep their purchasing power constant in 2023. What raise (in \%) would you request from your employer if a) Expectations are fully anchored, and the unemployment rate is constant between 2022 and 2023?