Describe how each of the following will affect the equilibrium price level(P) and real output(Y) in the short run(Assume the economy is initially in the long-run equilibrium.)

(a) A reduction in the real interest rate
(b) A widespread fear of deep recession on the part of consumers
(c) An increase in the average wage rate

To analyze how the given factors will affect the equilibrium price level (P) and real output (Y) in the short run, we will use the AD-AS model. In this model, the aggregate demand (AD) curve represents the relationship between the overall price level and the quantity of real output demanded, while the aggregate supply (AS) curve represents the relationship between the overall price level and the quantity of real output supplied.

(a) A reduction in the real interest rate:
When the real interest rate decreases, it tends to stimulate borrowing and investment. This leads to an increase in consumer spending and business investment, which in turn increases aggregate demand (AD). As a result, the AD curve shifts to the right, causing both the equilibrium price level (P) and real output (Y) to increase in the short run.

(b) A widespread fear of deep recession on the part of consumers:
If consumers have a widespread fear of a deep recession, they are likely to reduce their spending and increase their saving as a precaution. This leads to a decrease in aggregate demand (AD), as there is less demand for goods and services. Consequently, the AD curve shifts to the left, resulting in a reduction in both the equilibrium price level (P) and real output (Y) in the short run.

(c) An increase in the average wage rate:
When the average wage rate increases, it raises the production costs for businesses. As a result, the aggregate supply (AS) curve shifts to the left, indicating that businesses are willing to supply a smaller quantity of real output at each price level. This reduction in the quantity of real output supplied leads to a decrease in the equilibrium real output (Y) in the short run. However, the effect on the equilibrium price level (P) is ambiguous. It depends on the relative magnitude of the shift in the AS curve compared to the shift in the AD curve. If the decrease in aggregate supply outweighs the decrease in aggregate demand, the price level may increase. Conversely, if the decrease in aggregate demand is greater, the price level may decrease.

In summary, a reduction in the real interest rate generally increases both the equilibrium price level and real output, a widespread fear of deep recession decreases both the equilibrium price level and real output, and an increase in the average wage rate reduces real output while having an ambiguous effect on the equilibrium price level.