Chapter 8
You are given the following equations for the aggregate demand (AD) and short-run aggregate supply (SAS) curves: AD: Y = 1.25Aᴩ + 2.5Mˢ/P SAS: Y = 11,250 - 20W + 1,000P where Y is real GDP, Aᴩ is the amount of autonomous planned spending that is independent of the interest rate, Mˢ is the nominal money supply, P is the price level, and W is the nominal wage rate. Assume that Aᴩ equals 5,000, Mˢ equals 2,000, W equals 50, and natural real GDP, Yᴺ, equals 11,250.
Use the values for the amounts of autonomous planned spending that is independent of the interest rate and the nominal money supply to derive the equation for the aggregate demand curve. Compute the amount of aggregate demand when the price level equals 2.0, 1.25, 1.0, 0.8, and 0.5. Graph the aggregate demand curve.
Answer: The equation for aggregate demand is Y = 6,250 + 5,000/P.
See below graph for aggregate demand curve.
Price Level |2.0 |1.25 |1.0 |0.8 |0.5 | |Aggregate Demand |8,750 |10,250 |11,250 |12,500 |16,250 | |
Derive the equation for the short-run aggregate supply curve, given that the nominal wage rate equals 50. Compute the amount of short-run aggregate supply when the price level equals 2.0, 1.25, 1.0, 0.8, and 0.5. Graph the short-run aggregate supply curve.
Answer: The equation for the short-run aggregate supply curve is Y = 10,250 + 1,000P.
See below graph for short-run aggregate supply curve.
Price Level |2.0 |1.25 |1.0 |0.8 |0.5 | |Short-Run Aggregate Supply |12,250 |11,500 |11,250 |11,050 |10,750 | |
Given your answers to parts a and b, explain what the short-run and long-run equilibrium levels of real GDP and the price level are.
Answer: Short-Run Equilibrium Price Level = 1
Short-Run Equilibrium Level of Real GDP = 10,490
Long-Run Equilibrium Price Level = 11,250
Long-Run Equilibrium Level of Real GDP = 1
