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This is an individual assignment. You are expected to complete it on your own w...
Oct 3, 2024
Solution
a
Compute Nominal GDP: Nominal GDP is calculated by multiplying the price of each good by its quantity produced in each year. For 2020, Nominal GDP = (1 * 1000) + (2 * 1000) = 3000. For 2021, Nominal GDP = (1 * 1100) + (3 * 1200) = 3900. For 2022, Nominal GDP = (1 * 1210) + (4 * 1440) = 6340
b
Compute Real GDP: Real GDP is calculated using the base year prices (2020). For 2020, Real GDP = 3000. For 2021, Real GDP = (1 * 1100) + (2 * 1200) = 2700. For 2022, Real GDP = (1 * 1210) + (2 * 1440) = 3290
c
Compute Growth Rate in Real GDP: The growth rate is calculated as (Real GDP in current year - Real GDP in previous year) / Real GDP in previous year. From 2020 to 2021: Growth Rate = (2700 - 3000) / 3000 = -0.1 or -10%. From 2021 to 2022: Growth Rate = (3290 - 2700) / 2700 = 0.2185 or 21.85%
d
Compute Real GDP Growth Rate using Chain-Type Method: The chain-type growth rate is calculated using the formula: Growth Rate = (Real GDP in current year / Real GDP in previous year) - 1. From 2020 to 2021: Growth Rate = (2700 / 3000) - 1 = -0.1 or -10%. From 2021 to 2022: Growth Rate = (3290 / 2700) - 1 = 0.2185 or 21.85%. The growth rates calculated in part c do not significantly differ from those in part d, indicating that the growth rates are consistent
e
Calculate Real GDP in Chained 2020 Dollars: Using the growth rates derived in part d, Real GDP for 2021 = 3000 * (1 - 0.1) = 2700 and for 2022 = 2700 * (1 + 0.2185) = 3290
Answer
Nominal GDPs: 2020: 3000, 2021: 3900, 2022: 6340; Real GDPs: 2020: 3000, 2021: 2700, 2022: 3290; Growth Rates: 2020-2021: -10%, 2021-2022: 21.85%; Chained Real GDPs: 2021: 2700, 2022: 3290
Key Concept
Nominal GDP vs. Real GDP: Nominal GDP measures a country's economic output without adjusting for inflation, while Real GDP adjusts for inflation to reflect the true value of goods and services.
Explanation
The calculations show how to derive both Nominal and Real GDP, as well as growth rates, which are essential for understanding economic performance over time.
Solution
a
To find the equilibrium income Y Y , we set Y=C+I+G Y = C + I + G . First, we calculate consumption C C using the consumption function C=a+b(Y−T) C = a + b(Y - T) . Substituting the values: C=200+0.8(Y−200) C = 200 + 0.8(Y - 200) . Thus, Y=(200+0.8(Y−200))+200+200 Y = (200 + 0.8(Y - 200)) + 200 + 200 . Solving this gives Y=1000 Y = 1000 and C=800 C = 800
b
Autonomous spending is the sum of autonomous consumption a a , investment I0 I_0 , and government spending G G . Thus, Autonomous Spending=a+I0+G=200+200+200=600 \text{Autonomous Spending} = a + I_0 + G = 200 + 200 + 200 = 600 . The multiplier k k is calculated as k=11−b=11−0.8=5 k = \frac{1}{1 - b} = \frac{1}{1 - 0.8} = 5
c
With foreign trade, the import function is IM=0.05(Y−T) IM = 0.05(Y - T) . The new equilibrium income is calculated as Y=C+I+G−IM Y = C + I + G - IM . Substituting the values gives Y=(200+0.8(Y−200))+200+200−0.05(Y−200) Y = (200 + 0.8(Y - 200)) + 200 + 200 - 0.05(Y - 200) . Solving this results in a new income of Y=950 Y = 950 . The new autonomous spending is 600−0.05(950−200)=600−37.5=562.5 600 - 0.05(950 - 200) = 600 - 37.5 = 562.5 and the new multiplier remains 5 5
d
The Demand-Output diagram would show the initial equilibrium at Y=1000 Y = 1000 and the new equilibrium at Y=950 Y = 950 after trade opens. The adjustment process would illustrate a leftward shift in the aggregate demand curve due to increased imports
e
To maintain the income level at Y=1000 Y = 1000 with a balanced budget, the government must increase both G G and T T equally. The required increase can be calculated by setting the new G G and T T such that Y=C+I+G Y = C + I + G holds true. The exact amount depends on the new autonomous spending and the multiplier
Answer
Equilibrium income is Y=1000 Y = 1000 , consumption C=800 C = 800 , autonomous spending =600 = 600 , and the multiplier =5 = 5 . After trade, new income =950 = 950 and new autonomous spending =562.5 = 562.5 .
Key Concept
The equilibrium income in a closed economy is determined by the aggregate demand, which includes consumption, investment, and government spending.
Explanation
The calculations show how changes in government spending and foreign trade impact the equilibrium income and consumption levels in the economy. The multiplier effect amplifies the impact of autonomous spending on overall income.
Solution
a
To find the interest rate in equilibrium, we set the money demand equal to the money supply. The money demand function is given by Md=Y×(1.2−10i) M^d = Y \times (1.2 - 10i) . Given Y=6000 Y = 6000 billion and the monetary base M=300 M = 300 billion, we can express the money supply as M=Mdθ M = \frac{M^d}{\theta} where θ=0.125 \theta = 0.125 . Thus, Ms=3000.125=2400 M_s = \frac{300}{0.125} = 2400 billion. Setting Md=Ms M^d = M_s , we have 2400=6000×(1.2−10i) 2400 = 6000 \times (1.2 - 10i) . Solving for i i gives i=0.04 i = 0.04 or 4% 4\%
b
To achieve a target interest rate of 6% 6\% through open market operations (OMO), the central bank needs to decrease the money supply. The new money demand at i=0.06 i = 0.06 is Md=6000×(1.2−10×0.06)=6000×0.6=3600 M^d = 6000 \times (1.2 - 10 \times 0.06) = 6000 \times 0.6 = 3600 billion. The central bank must increase the monetary base to match this demand. The required monetary base is M=Ms×θ=3600×0.125=450 M = M_s \times \theta = 3600 \times 0.125 = 450 billion. Thus, the central bank needs to conduct OMO to increase the monetary base from 300 300 billion to 450 450 billion
c
If people hold currency amounting to 15 \frac{1}{5} of their total money demand, the money demand becomes Md=6000×(1.2−10i) M^d = 6000 \times (1.2 - 10i) with i i calculated as before. The total money demand is 2400 2400 billion, and currency held is 15×2400=480 \frac{1}{5} \times 2400 = 480 billion. The money supply is then Ms=M+C=300+480=780 M_s = M + C = 300 + 480 = 780 billion. The interest rate can be recalculated using the money demand function
d
If people hold 110 \frac{1}{10} of their total money demand as currency, the money supply will be less than in part c. This is because holding less currency means more money is available in deposits, which increases the money multiplier effect, leading to a lower overall money supply
e
If people hold 100 100 billion in currency, the money supply can be calculated as Ms=M+C=300+100=400 M_s = M + C = 300 + 100 = 400 billion. The balance sheet of the central bank would show assets (government bonds) and liabilities (currency held and reserves). The total assets would equal the total liabilities, maintaining the balance
Answer
Interest rate in equilibrium is 4% 4\% ; monetary base needed for 6% 6\% is 450 450 billion; money supply with currency holdings is 780 780 billion; holding 110 \frac{1}{10} reduces money supply; total money supply with 100 100 billion currency is 400 400 billion.
Key Concept
The relationship between money demand, money supply, and interest rates in an economy.
Explanation
The calculations illustrate how changes in monetary policy and currency holdings affect the equilibrium interest rate and money supply.
Solution
a
To find the IS equation, we start with the goods market equations. The consumption function is given by C=100+0.5(Y−T) C = 100 + 0.5(Y - T) where T=100 T = 100 . Thus, C=100+0.5(Y−100)=100+0.5Y−50=50+0.5Y C = 100 + 0.5(Y - 100) = 100 + 0.5Y - 50 = 50 + 0.5Y . The investment function is I=50−2i I = 50 - 2i . The total output in the goods market is Y=C+I+G Y = C + I + G . Substituting the values, we have: Y=(50+0.5Y)+(50−2i)+200 Y = (50 + 0.5Y) + (50 - 2i) + 200 Simplifying gives: Y−0.5Y=300−2i  ⟹  0.5Y=300−2i  ⟹  Y=600−4i Y - 0.5Y = 300 - 2i \implies 0.5Y = 300 - 2i \implies Y = 600 - 4i
b
The LM equation is derived from the money market. Given MS=4000 M^S = 4000 and P=10 P = 10 , we have MD=P⋅L(Y,i)=10(Y−6i) M^D = P \cdot L(Y, i) = 10(Y - 6i) . Setting MS=MD M^S = M^D : 4000=10(Y−6i)  ⟹  400=Y−6i  ⟹  Y=400+6i 4000 = 10(Y - 6i) \implies 400 = Y - 6i \implies Y = 400 + 6i
c
To find the equilibrium real output, we set the IS and LM equations equal: 600−4i=400+6i 600 - 4i = 400 + 6i Solving for i i : 600−400=10i  ⟹  200=10i  ⟹  i=20% 600 - 400 = 10i \implies 200 = 10i \implies i = 20\% Substituting i i back into the IS equation: Y=600−4(20)=600−80=520 Y = 600 - 4(20) = 600 - 80 = 520 At this output level, equilibrium is not immediately attained in the Money Market because MS M^S does not equal MD M^D . The central bank needs to adjust the money supply to restore equilibrium
d
To find the levels of consumption and investment at equilibrium Y=520 Y = 520 : C=50+0.5(520)=50+260=310 C = 50 + 0.5(520) = 50 + 260 = 310 I=50−2(20)=50−40=10 I = 50 - 2(20) = 50 - 40 = 10 To show that investment equals national saving, we calculate national saving S=Y−C−G S = Y - C - G : S=520−310−200=10 S = 520 - 310 - 200 = 10 Thus, I=S=10 I = S = 10
e
With an expansionary fiscal policy increasing government spending by 50%, new G=200+100=300 G = 200 + 100 = 300 . The new IS equation becomes: Y=(50+0.5Y)+(50−2i)+300 Y = (50 + 0.5Y) + (50 - 2i) + 300 Solving gives: Y−0.5Y=400−2i  ⟹  0.5Y=400−2i  ⟹  Y=800−4i Y - 0.5Y = 400 - 2i \implies 0.5Y = 400 - 2i \implies Y = 800 - 4i Setting this equal to the LM equation Y=400+6i Y = 400 + 6i : 800−4i=400+6i  ⟹  400=10i  ⟹  i=40% 800 - 4i = 400 + 6i \implies 400 = 10i \implies i = 40\% Substituting back gives: Y=800−4(40)=800−160=640 Y = 800 - 4(40) = 800 - 160 = 640 Using the output multiplier k=11−MPC=11−0.5=2 k = \frac{1}{1 - MPC} = \frac{1}{1 - 0.5} = 2 , the change in output is: ΔY=k⋅ΔG=2⋅100=200  ⟹  Ynew=520+200=720 \Delta Y = k \cdot \Delta G = 2 \cdot 100 = 200 \implies Y_{new} = 520 + 200 = 720
Answer
The IS equation is Y=600−4i Y = 600 - 4i , the LM equation is Y=400+6i Y = 400 + 6i , equilibrium output is Y=520 Y = 520 , consumption C=310 C = 310 , investment I=10 I = 10 , and new equilibrium after fiscal policy is Y=640 Y = 640 .
Key Concept
The IS-LM model illustrates the interaction between the goods market and the money market, determining equilibrium output and interest rates.
Explanation
The solution involves deriving the IS and LM equations, finding equilibrium output, and analyzing the effects of fiscal policy on the economy.
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