This is an economics question, not a mathematics question.  But I put it an AI
site for you. You can go there yourself:

https://poe.com/chat/ 

AI still makes lots of errors in mathematics questions, but
hopefully it does a better job with economics questions.

-------------------------------------------------------

The Four Phases of the Business Cycle
The business cycle consists of four key phases:

1. Expansion (or Recovery):
   During this phase, economic activity increases, marked by rising GDP,
   employment, and income levels.
   Businesses invest more, consumer confidence grows, and demand for goods and
   services strengthens.
   Inflation may begin to rise as the economy moves closer to full capacity.
2. Peak:
   This is the highest point of economic activity before a slowdown begins.
   Output, employment, and income are at their maximum levels, but growth slows
   as capacity constraints and inflationary pressures emerge.
3. Contraction (or Recession):
   Economic activity declines, with falling GDP, reduced employment, and lower
   consumer spending.
   Businesses cut back on investment and production due to weakened demand.
   If the contraction is prolonged and severe, it may lead to a depression.
4. Trough:
   The lowest point of the business cycle, where economic activity bottoms out.
   Unemployment is high, and output is at its lowest level.
   This phase sets the stage for the next expansion as recovery efforts take
   hold.

Length of Business Cycles
The length of business cycles varies widely, depending on economic conditions,
government policies, and external factors. Historically:

   Business cycles in advanced economies have lasted anywhere from a few years
   to over a decade.
   The average duration of a full cycle (from peak to peak or trough to trough)
   is approximately 5  -  10 years.

Seasonal Variations and Secular Trends
Seasonal variations and secular trends complicate the measurement of the
business cycle in the following ways:
1. Seasonal Variations:
   Short-term fluctuations occur due to predictable seasonal changes, such as
   increased retail activity during holidays or agricultural cycles.
   These fluctuations can mask underlying trends in economic activity, making it
   harder to identify the true phase of the business cycle.
2. Secular Trends:
   Long-term growth trends, driven by factors like technological progress,
   population growth, or structural changes in the economy, can obscure cyclical
   movements.
   For instance, an economy experiencing long-term growth may still go through
   periodic contractions, which could be overlooked if the focus is solely on
   the upward trend.

To address these issues, economists use techniques like seasonal adjustment and
trend analysis to isolate cyclical movements.

Why Capital Goods and Consumer Durables Are Affected More
The business cycle impacts industries unevenly, with capital goods and consumer
durable goods industries being more severely affected than industries producing
non-durable goods. Here's why:

1. Capital Goods:
   These goods (e.g., machinery, equipment) are often purchased by businesses
   for long-term use.
   During a contraction, businesses reduce investment in capital goods due to
   uncertainty and lower profits, causing a sharp decline in demand.
2. Consumer Durables:
   Durable goods (e.g., cars, appliances) are expensive items that consumers can
   postpone purchasing during economic downturns.
   As household incomes decline or become uncertain, consumers prioritize
   essential spending over big-ticket items.
3. Non-Durable Goods:
   In contrast, industries producing non-durable goods (e.g., food, toiletries)
   are less affected because these items are essential and consumed regularly,
   regardless of the economy's state.
   Demand for non-durables tends to remain relatively stable even during
   recessions.

This disparity in impact underscores the cyclical sensitivity of industries tied
to discretionary and investment-related spending.

Edwin