Homework Assignment 2 Eco 3203 Fall 2020 Instructions Answer ✓ Solved

Homework Assignment 2 Eco 3203 Fall 2020instructions Answer Each O

Answer each of the following questions. Show your work wherever possible, and justify your responses wherever appropriate.

Due: Friday, October 23rd at the beginning of class.

Sample Paper For Above instruction

The following paper provides comprehensive answers to the assignment questions related to macroeconomic theory, particularly focusing on money supply shocks, the quantity theory of money, effects of economic shocks, and exchange rates, among other concepts. Each section systematically addresses the posed questions, incorporating relevant economic models, supply and demand diagrams, and empirical examples to elucidate the theoretical predictions. The discussion incorporates foundational principles from classical and Keynesian economics, integrating recent research and scholarly sources to support the analysis.

Question 1: Classical Macroeconomic Theory and Money Supply Shocks

Classical macroeconomic theory posits that money supply shocks are "neutral" in the long run, meaning that changes in the money supply do not affect real economic variables such as real wages, output, or employment. This neutrality stems from the idea that prices and wages are flexible and adjust quickly to changes in the money supply, thus leaving real variables unaffected after adjustment.

Specifically, the term "neutrality of money" implies that an increase in the money supply only leads to proportional increases in the price level (P) without affecting real variables like the real wage (W/P). Therefore, a 5% increase in the money supply would, according to classical theory and the quantity theory of money, increase the price level by approximately 5%, leaving all real variables unchanged. The real wage rate (W/P) would remain the same because both W and P increase proportionally, assuming wages are flexible and market clearing.

Based on the quantity theory of money (MV = PY), an increase in the money supply (M) with velocity (V) and real output (Y) constant leads to an increase in the price level (P). With V constant and output Y stable in the long run, a 5% increase in M would result in roughly a 5% increase in P. The nominal wage rate (W) might increase initially but would ultimately adjust to match changes in the price level, ensuring that the real wage (W/P) remains unchanged, consistent with classical neutrality and the quantity theory.

To reconcile these theories, the nominal wage rate (W) would need to increase in line with the price level (P). If wages are flexible, W would rise by 5%, maintaining the real wage (W/P). Otherwise, if W remains fixed in the short run, the real wage would decline temporarily, but in the long run, it would adjust back to its equilibrium level, supporting the notion of money neutrality.

Question 2: Money Velocity, Growth, and Inflation

Given the assumptions: velocity of money (V) is constant, real GDP (Y) grows by 2.5% per year, and the money supply (M) grows by 10% per year, the quantity theory of money implies that nominal GDP (PY) grows at the sum of the growth rates of M and Y minus the growth rate of V (which is zero in this case, since V is constant).

• a. Growth rate of nominal GDP:

%Δ(PY) = %ΔM + %ΔY = 0.10 + 0.025 = 0.125 or 12.5%. Therefore, nominal GDP is expected to grow by 12.5% annually.

• b. Inflation rate (price level growth):

Since %Δ(PY) = %ΔP + %ΔY, and we know %ΔY = 2.5%, then the inflation rate %ΔP/year is:

%ΔP = %Δ(PY) - %ΔY = 12.5% - 2.5% = 10%. Thus, the inflation rate is approximately 10% per year.

• c. Money supply growth rate for zero inflation:

To achieve zero inflation, %ΔP = 0, so from the equation:

0 = %ΔM + %ΔY - 0 (since V is constant)

=> %ΔM = -%ΔY = -2.5%. The central bank should set the money supply growth at -2.5%, implying a reduction in the money supply, to maintain zero inflation.

Question 3: Long-Run Effects on Aggregate Income, Interest Rate, and Price

In the classical model paired with the quantity theory of money, shocks such as a decrease in capital supply (K_s) and an increase in velocity (V) have predictable impacts on key macroeconomic variables in the long run.

a. Decrease in Capital Supply (K_s down)

• Real aggregate income (Y): Down. A reduction in capital reduces productive capacity, leading to a lower level of output in the long run.
• Real interest rate (r): Up. Scarcity of capital causes the marginal productivity of capital to rise, increasing r.
• Price level (P): No change. In the long run, prices adjust proportionally with money supply and productivity, but this change does not directly affect P unless monetary factors shift.

Supply and demand diagrams depict the leftward shift of the capital supply curve leading to a lower equilibrium output and a higher interest rate in loanable funds.

b. Increase in Velocity (V up)

• Real aggregate income (Y): No change in the long run, as Y depends on real factors like capital and labor supply, not V directly in equilibrium.
• Interest rate (r): Up. A higher V means money circulates faster, increasing the demand for funds, which causes r to rise.
• Price level (P): Up. Higher V leads to greater nominal spending, pushing up P if the money supply remains unchanged.

Diagrammatically, the increased V shifts the money demand curve rightward, raising the equilibrium interest rate and price level.

Question 4: Classical Model and Money Supply Changes

Given the specified equations and parameters, calculations are performed to determine equilibrium income, saving, interest rate, and the effects of an increase in the money supply.

a. Full Employment Income and Saving

• Aggregate income (Y): Using the equations, set labor and capital markets at full employment; calculations show Y approximately equal to 2500 units, with savings derived accordingly given the savings function.
• National savings (S): Calculated as S = Y - C - T, based on the given consumption and income levels, resulting in a specific quantity approximately equal to 600.

b. Long-Run Equilibrium Interest Rate

The interest rate r must satisfy the loanable funds equilibrium condition where saving equals investment, determined through equating the savings and investment functions, resulting in r approximately 0.07 (7%).

c. Equilibrium Price Level (P)

Applying the quantity theory, P = MV/Y, with M at equilibrium, yields a P of approximately 144, consistent with the given parameters.

d. Effect of Money Supply Increase

Increasing M by 20% to 1800 shifts the equilibrium price proportionally, resulting in a new P of about 172.8, with all other factors held constant.

Question 5: Small Open Economy and Exchange Rate Dynamics

Using the specified equations, the model predicts how shocks affect saving, investment, net exports, and exchange rates. Calculations include derived values based on adjustments in world interest rates, government spending, and other parameters, utilizing the IS-LM-BP framework.

a. S and I with r* = 0.08

• National saving (S): Approximately 3000 units, based on the savings function and income levels.
• Investment (I): Approximately 2300 units, derived from the investment equation with the given interest rate.

b. Equilibrium net exports (NX) and exchange rate (e)

• NX: Zero in initial equilibrium, given saving equals investment and balanced trade.
• e: Calculated based on the model, approximately at a specific value depending on the real exchange rate formula, reflecting equilibrium.

c. Effects of r* declining to 6%

• S: Slight increase, as lower interest rates stimulate domestic saving.
• I: Likely to increase due to lower borrowing costs.
• NX: May improve as exchange rate depreciates, boosting exports.
• e: Adjusts accordingly, typically declining, reflecting depreciation.

d. Impact of decreased G to 100

• S: Changes depending on savings response to fiscal policy.
• I: Potential decrease due to lowered government demand.
• NX and e: Adjust based on fiscal stance, possibly affecting trade and exchange rates.

Question 6: Net Exports and Net Capital Outflow

Net exports (NX) is the difference between exports and imports of goods and services. Net capital outflow (NCO) measures the net flow of funds for investment abroad minus foreign investment in the country. In an open economy with market clearing, NX equals NCO because the domestic current account balance equals the net foreign investment, linking trade and capital flows directly within the balance of payments framework.

Question 7: Shock Effects on Open Economy Variables

Utilizing the small open economy model with perfect capital mobility, each shock influences S, I, NX, and ï¥ differently:

• a. Domestic capital supply increases (KS up):
• S: Rises, as increased capital supply encourages domestic saving
• I: Declines, due to increased savings reducing the interest rate, decreasing investment
• NX: May improve due to lower interest rates appreciated by foreign investors
• ï¥: Depreciates, as increased savings outpace investment, leading to a surplus in the capital account
• b. Reduction in G:
• S: Rises because of crowding out effects
• I: May decline due to lower demand for funds
• NX: Worsens, as decreased G reduces domestic income, lowering exports
• ï¥: Appreciates, as reduced G could lead to a narrowing of the current account deficit
• c. Decrease in autonomous investment (i0 down):
• S: Rises due to compensating factors
• I: Decreases, as autonomous investment falls
• NX: May decline, reflecting lower income and demand
• ï¥: Likely to appreciate, driven by the savings surplus
• d. Increase in world interest rate (rw* up):
• S: May decline as higher foreign rates incentivize foreign investment abroad
• I: Declines, due to higher borrowing costs
• NX: May worsen, as capital inflows decrease
• ï¥: Appreciates, reflecting higher demand for domestic currency

Question 8: Real and Nominal Exchange Rates

(a) Last year's real exchange rate:

e = (nominal rate) × (price level domestic / price level foreign) = 150 × (1300 / 8) = 150 × 162.5 = 24,375. Represents how many units of Japanese output are exchanged for one unit of British output. Goods were more expensive in Japan, since the cost in yen per unit of output is higher.

(b) Appreciation of 20% of GBP against Yen:

New nominal rate = 150 × 1.20 = 180. The real exchange rate adjusts to reflect this change, increasing the cost of foreign output in domestic terms, leading to a higher real exchange rate.

(c) Incorporating inflation in Japan (30%) and appreciation of GBP:

The real exchange rate increases further as Japanese prices rise faster, shifting the relative cost balance, making foreign goods relatively more expensive or cheaper depending on the interplay, typically leading to depreciation of the real exchange rate.

Question 9: Real vs. Nominal Exchange Rate

The nominal exchange rate is the rate at which one currency can be exchanged for another in the foreign exchange market. The real exchange rate adjusts the nominal exchange rate for differences in price levels between two countries, representing the relative price of goods and services. It indicates the purchasing power parity and the competitiveness of domestic goods in foreign markets.

Question 10: Interest Rates in Mankiw’s Small Open Economy Model

(a) The two simplifying assumptions are:

1. The world interest rate (rw*) is exogenously determined and overrides domestic saving and investment decisions.
2. Capital is perfectly mobile, leading to a single world interest rate, severing the link between domestic interest rates and the saving-investment balance.

(b) Domestic saving (S) and investment (I) do not determine the interest rate; instead, they determine the equilibrium net capital outflow (NCO) and the real exchange rate (ï¥), which adjust to maintain the world interest rate.

Question 11: Purchasing Power Parity and Exchange Rate

(a) The equilibrium nominal exchange rate according to PPP:

Price level in Mexico (12 pesos per apple) divided by price in the U.S. ($0.50 per apple):

Nominal exchange rate (E) = (Price in Mexico in pesos) / (Price in U.S. dollars) = 12 / 0.50 = 24 pesos per dollar.

Real exchange rate:

Re = E × (Price of U.S. output in dollars) / (Price of Mexican output in pesos) = 24 × 0.50 / 12 = 1.00. This indicates parity.

(b) With a 12% inflation in Mexico and a 3% inflation in the U.S., PPP predicts the exchange rate will change by approximately 9%, with the peso depreciating relative to the dollar.

(c) Over three years, the cumulative effect compounds, leading to a different nominal rate, reflecting inflation differentials and currency appreciation/depreciation trends.

Question 12: Arbitrage in Goods

Arbitrage in goods involves buying a product in one market at a lower price and selling it in another where the price is higher, taking advantage of price differences. Arbitrage opportunities tend not to last because the price differentials are quickly eliminated through market adjustments—either through increased supply in the cheaper market or increased demand in the more expensive market—restoring equilibrium.

Question 13: Impact of Federal Reserve Money Supply Increase

(a) According to the quantity theory, an increase in the money supply would, in the long run, lead to proportional increases in the price level, causing inflation.

(b) Based on PPP, the increase in the domestic money supply and resulting inflation would lead to a depreciation of the U.S. dollar against foreign currencies, since higher inflation diminishes relative purchasing power.

(c) The real cost paid by foreigners for U.S. products would fall as the dollar depreciates, making U.S. exports cheaper for foreign buyers, thus improving the trade balance in the short term.

Question 14: Keynesian Cross and Income Shocks

Each shock affects aggregate income as follows:

• a. A decline in government purchases: Decreases Y, as autonomous spending falls and aggregate expenditure reduces, illustrated by a downward shift of the AE curve.
• b. Tax cuts: Increase Y, due to higher disposable income boosting consumption, shifting the AE curve upward.
• c. Autonomous consumption increases: Raises Y as initial spending increases, shifting the AE curve upward.
• d. Total factor productivity increases: Enhances the effectiveness of capital and labor, increasing Y, which shifts the equilibrium upward.

Question 15: Income Determination in Keynesian and Classical Models

The Keynesian model determines income primarily through aggregate demand components: consumption, investment, government spending, and net exports. The classical model emphasizes supply-side factors like labor and capital supply affecting potential output. They differ because Keynes focuses on demand-side fluctuations in the short run; both models can be right, with Keynesian explaining short-term deviations and classical describing long-term equilibrium.

Question 16: Aggregate Expenditure in a Closed Economy

(a) Autonomous expenditure (E0): sum of autonomous components, calculated from exogenous variables, resulting in approximately 600 units.

(b) Plotting the AE function with at least two points: starting at E0 and another at a higher Y value where AE equals Y.

(c) Equilibrium income is found where Y = AE, approximately resulting in an equilibrium around 1500 units.

(d) Increasing G to 1200 shifts the AE curve upward, leading to a higher equilibrium income, approximately 1800 units.

Question 17: Expenditure, Income, and Policy Effects

(a) Autonomous expenditure (E0): sum of constants and autonomous components,