Suppose the economy is in a long-run equilibrium. a. Draw a diagram to illustrate the state of the economy. Be sure to show aggregate demand, short-run aggregate supply, and long-run aggregate supply. b. Now suppose that a stock market crash causes aggregate demand to fall. Use your diagram to show what happens to output and the price level in the short run. What happens to the unemployment rate? c. Use the sticky-wage theory of aggregate supply to explain what happens to output and the price level in the long run (assuming no change in policy). What role does the expected price level play in this adjustment? Be sure to illustrate your analysis in a graph.

Understanding the forces of aggregate demand and supply is crucial for analyzing economic stability and growth. Aggregate demand (AD) encompasses the total amount of goods and services demanded across all levels of an economy at a given overall price level and in a given period. It reflects consumers' purchases, business investments, government spending, and the net exports of a nation.

Conversely, aggregate supply represents the total output of goods and services that producers are willing and able to supply at a given price level. It’s divided into short-run aggregate supply (SRAS) and long-run aggregate supply (LRAS), each with distinct characteristics. The equilibrium where these two curves intersect signifies a balance between the quantity of goods and services supplied and demanded.

The short-run aggregate supply (SRAS) curve is upward sloping, reflecting that, in the short-term, as prices rise, the quantity of goods and services supplied increases. This is partly because of the presence of sticky wages and prices - that is, they don't adjust instantly to changes in economic conditions.

Other short-term factors affecting SRAS include misperceptions about price changes, adjustments in resource prices, and temporary levels of productivity. During short-term periods, firms will meet the increased demand by utilizing their existing workforce and machinery more intensely.

The long-run aggregate supply curve is vertical, indicating that in the long-term, the total output is at its maximum sustainable level, regardless of price level changes. This is attributable to the economy's resources—such as labor, capital, and technology—being fully employed.

In the long-run, an economy is expected to produce at its full potential, which reflects the natural rate of output where all resources are optimally used. Shifts in the LRAS can occur due to changes in these resources, such as technological advancements or changes in the labor force.

The sticky-wage theory suggests that nominal wages are inflexible in the short-run and do not adjust immediately to changes in economic conditions, such as fluctuations in the price level or in the overall demand for labor.

When the overall price level declines, the purchasing power of fixed nominal wages increases, leading firms to reduce employment to lower costs, since they're paying relatively more for labor than intended. Over time, nominal wages will adjust downwards, allowing the short-run aggregate supply to shift and the economy to return to the natural level of employment and output.

A stock market crash has a significant impact on the economy, primarily through the wealth effect and investment channels. As stock values plummet, people feel poorer, which dampens consumer confidence and reduces spending.

Similarly, businesses' ability to raise capital through equity is hampered, resulting in decreased investment. Both factors lead to a fall in aggregate demand, which, according to the AD-AS model, results in decreased output and unemployment in the short-run, as seen by a leftward shift of the AD curve.

Full employment is a term used to describe a situation where all available labor resources that are willing and able to work at the prevailing wages are employed. It's important to note that this does not mean zero unemployment, as there will always be some level of frictional and structural unemployment.

The notion of full employment aligns closely with the natural rate of output represented by the intersection of the LRAS and AD curves, where the economy is stable with an unemployment rate that is consistent with 'full employment'.

The natural rate of unemployment is the level of unemployment consistent with a stable rate of inflation. It comprises frictional unemployment, which occurs when workers are between jobs, and structural unemployment, which results when there’s a mismatch between workers’ skills and job requirements.

The natural rate of unemployment does not include cyclical unemployment that arises during downturns. Achieving full employment means reaching this natural rate, where only frictional and structural unemployment persist, as opposed to higher cyclical unemployment resulting from economic fluctuations.