Final answer:
b. 1.3
To find the price level, we need to equate the real money demand to the nominal money supply.
Step-by-step explanation:
To find the price level, we need to equate the real money demand to the nominal money supply. Given the real money demand function, we substitute the given values of real output (Y), real interest rate (r + piᵉ), and the expected inflation rate (piᵉ). Assuming constant velocity of money, we have:
To solve for the price level: 1. Substitute the given values into our real money demand equation: $$ L = 0.8Y - 100,000(r + \pi^e) $$ Here, \( Y = 15,000 \), \( r = 0.02 \), and \( \pi^e = 0.01 \). Therefore, the calculation becomes: $$ L = 0.8(15,000) - 100,000(0.02 + 0.01) $$ $$ L = 12,000 - 100,000(0.03) $$ $$ L = 12,000 - 3,000 $$ $$ L = 9,000 $$ 2. The nominal money supply (Ms) equals money demand (L) times the price level (P): $$ Ms = L \times P $$ We know the nominal money supply is \( Ms = 12,000 \) and we just computed \( L = 9,000 \). 3.
To find the price level (P), we rearrange the equation to solve for P: $$ P = \frac{Ms}{L} $$ Substitute the values we have: $$ P = \frac{12,000}{9,000} $$ 4. Now, performing the division to find the price level: $$ P = \frac{12,000}{9,000} = \frac{4}{3} \approx 1.3333 $$ 5. Finally, we look at the options provided to find the closest value: a. 1.2 b. 1.3 c. 1.4 d. 1.5 The value we calculated, 1.3333, is closest to option b, which is 1.3. Therefore, the price level is **1.3**.