Under the assumption that expectations are adaptive, the y-intercept (when the value on the x-axis equals 0) of the aggregate supply curve is always equal to:

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The question asks about the y-intercept of the aggregate supply curve under the assumption that expectations are adaptive, specifically when the value on the x-axis is 0. In reviewing the answer options, I’ll assess each possibility in light of adaptive expectations and the typical AS framework.

Option 1: '𝜋¯.' This represents a constant or steady-state value of inflation with no time subscript, effectively implying the intercept is a fixed long-run inflation rate. In the adaptive-expectations setting, the intercept usually incorporates current information and tends to move with the inflation process rather than stay fixed at a simple average. Therefore, this option fails to capture the dynamic, time-varying nature expected for the intercept when considering adaptive expectations.

Option 2: '𝜋t.' Here, the intercept would equal current inflation at time t. Under adaptive expectations, agents form expectations based on past inflation, and the short-run supply relationship typically shifts with anticipated inflation. Setting the intercept equal to instantaneous inflation ignores the lagged updating mechanism that adaptive expectations imply, making this choice inconsistent with the standard interpretation where the intercept reflects past information and adjustments.

Option 3: '𝜋t − 1.' This option expresses the intercept as current inflation minus one period ago, i.e., the lagged inflation effect. Under adaptive expectations, agents update expectational terms using previous period data, which often translates into a relationship where the intercept includes a lagged component. This aligns with the idea that the intercept of the AS curve, when x = 0, reflects information carried over from the prior period, consistent with adaptive expectations.

Option 4: '𝜋t − 1 + 𝑜¯t.' This adds an additional term '𝑜¯t' (perhaps representing an output gap or another shock term) to the lagged inflation. Including an extra shock term in the intercept goes beyond the classic adaptive-expectations setup for the AS intercept and introduces another moving part that is not typically described as the intercept under a clean adaptive framework. This makes it less likely to be the standard intercept value asked for in the question.

Option 5: '𝑌~t.' This symbol usually denotes a potential or trend-output level rather than an inflation-based intercept. Using output (Y~t) as the intercept would mix up the typical inflation-focused intercept in an AS framework and does not align with the conventional interpretation of the intercept in a Phillips- or AS-type equation under adaptive expectations.

Option 6: '𝑜¯t.' If this denotes a neutral or baseline shock term, it could be a contender only if the model explicitly defines the intercept to be this baseline. However, without a clear definition tying '𝑜¯t' to the standard adaptive-expectations intercept for the AS curve, this option seems ambiguous and unlikely to be the conventional intercept value under the standard formulation.

Option 7: '𝜋¯ + 𝑜¯t.' This combines a long-run or average inflation term with a baseline shock. While this could reflect a scenario where the intercept shifts with a constant component plus a shock, the question asks for the intercept under adaptive expectations in a standard setup. Therefore, this option tends to overcomplicate the intercept and is not the conventional, single-term intercept described in typical adaptive-expectations AS models.

In sum, among the listed choices, the one that best matches the standard interpretation of the y-intercept of the aggregate supply curve under adaptive expectations—capturing the lagged information from the previous period—is the option '𝜋t − 1.' This reflects the idea that the intercept is driven by the prior period’s inflation, consistent with agents updating expectations adaptively and the AS relation reacting to past information.

Under the assumption that expectations are adaptive, the y-intercept (when the value on the x-axis equals 0) of the aggregate supply curve is always equal to:Single choice

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