Question

An economy’s relationship between short-run equilibrium output and inflation (its aggregate demand curve) is described by the equation: Y = 13,000 – 20,000π. Initially, the inflation rate is 4 percent, or π = 0.04. Potential output Y* equals 12,000.

a. The short-run equilibrium output is_____________ .
b. The rate of inflation at the long-run equilibrium is _____________.

Answer 1

The short-run equilibrium output is 12,200, found by substituting the given inflation rate into the aggregate demand equation. The rate of inflation at the long-run equilibrium is 5%, which keeps the output at its potential level.

Step-by-step explanation:

To find the short-run equilibrium output, we substitute the initial inflation rate π = 0.04 into the aggregate demand curve equation, Y = 13,000 - 20,000π. This yields:

Y = 13,000 - 20,000(0.04) = 13,000 - 800 = 12,200.

For part b, since the long-run equilibrium output is at the potential output level, and in the long run, the aggregate supply curve is vertical, changes in inflation do not affect the output. Therefore, the economy produces at its potential regardless of the rate of inflation. In the equation Y = 13,000 - 20,000π, for Y to be equal to the potential output Y* of 12,000, π must be:

12,000 = 13,000 - 20,000π → 20,000π = 13,000 - 12,000 → 20,000π = 1,000 → π = 1,000 / 20,000 = 0.05 or 5%

This means the rate of inflation at the long-run equilibrium is 5%.

Answer 2

(a) 12,200

(b) 5%

Step-by-step explanation:

(a) Y = 13,000 - 20,000 (.04)

Y = 13,000 - 800

Y = 12,200

Therefore, the short run equilibrium output is 12,200.

(b) Y = 13,000 - 20,000π

Substituting the value of y* by 12,000

12,000 = 13,000 - 20,000π

20,000π = 13,000 - 12,000

π = (1,000 ÷ 20,000 ) × 100

π = 0.05 or 5 %

Therefore, the rate of inflation at the long-run equilibrium is 5%.