Assume that the Phillips curve for a given economy is given by:
π = πt-1 – 0.5 (ut – 0.06)
a. Explain the concept of the natural level of unemployment using the above Phillips curve.
b. draw the short-run and the long-run Phillips curve.
c. Suppose that the Central Bank wants to reduce the inflation rate in period t by 5%. According to the Phillips curve defined above explain the effects of this policy in the short-run. By considering the Okun’s law, what is the change in GDP that will be associated with the change in unemployment rate.
a. The concept of the natural level of unemployment can be understood using the Phillips curve equation. In the equation, π represents the inflation rate, ut represents the unemployment rate, and πt-1 represents the inflation rate in the previous period.
The natural level of unemployment is the level of unemployment that occurs when the economy is at its potential output or full employment. It is the rate of unemployment that is consistent with stable inflation over the long run. In the Phillips curve equation, when the actual unemployment rate (ut) is equal to the natural level of unemployment, the equation simplifies to:
π = πt-1 - 0.5(0 - 0.06)
= πt-1 + 0.03
In this case, the inflation rate is solely determined by the inflation rate in the previous period (πt-1). This means that there is no trade-off between inflation and unemployment when the economy is at its natural level of unemployment.
b. The short-run Phillips curve shows the relationship between inflation and unemployment in the short run, while the long-run Phillips curve shows the relationship in the long run.
In the short run, the Phillips curve is downward sloping, indicating a trade-off between inflation and unemployment. As unemployment decreases below the natural level, inflation tends to increase. Conversely, when unemployment is above the natural level, inflation tends to decrease.
In the long run, the Phillips curve is vertical or nearly vertical at the natural level of unemployment. This means that in the long run, there is no trade-off between inflation and unemployment. Changes in inflation are solely determined by other factors such as changes in aggregate demand, supply shocks, or monetary policy.
c. If the Central Bank wants to reduce the inflation rate by 5% in period t, it can do so by reducing inflation expectations in the economy. According to the Phillips curve defined above, this can be achieved by reducing the inflation rate in the previous period (πt-1).
In the short run, a reduction in the inflation rate by 5% will lead to a decrease in the inflation rate in period t. As a result, the Phillips curve equation becomes:
π = πt-1 - 0.5(ut - 0.06) - 0.5(0 - 0.06)
= πt-1 + 0.03 - 0.5ut + 0.03
This means that for a given level of unemployment, the inflation rate will decrease by 0.06 compared to the previous period.
According to Okun's law, there is a negative relationship between changes in the unemployment rate and changes in GDP. Specifically, for each 1% increase in the unemployment rate, GDP tends to decrease by approximately 2%. Therefore, if there is a decrease in the unemployment rate due to the reduction in inflation, GDP is expected to increase by a corresponding amount, assuming Okun's law holds true in this particular economy.
a. Show how the government budget deficit may worsens the Current Account (CA) deficit.
b. Consider an economy described by the following equations:
Y = C + I +G
Y = 5000
C(Y – T, r) = 1200 + 0.3(Y – T) – 50r
I(r) = 1500 – 50r
T = 1000
G = 1500
a. What are the equilibrium values of C, I, and r?
b. What are the values of private saving, public saving, and national saving?
c. Now assume there is a technological innovation that makes business want to invest more. It raises the investment equation to I(r) = 2000 – 50r. What are the new equilibrium values of C, I, and r?
d. What are the new values of private saving, public saving, and national saving?
a. The government budget deficit refers to the situation where government spending exceeds government revenue, leading to a negative balance in the government's budget. This deficit can worsen the current account deficit through several channels:
1. Increased government spending: When the government runs a budget deficit, it typically needs to finance this deficit by borrowing from domestic or foreign sources. This increase in borrowing can lead to an increase in demand for foreign currency, resulting in a depreciation of the domestic currency. A depreciation of the domestic currency makes imports more expensive and exports cheaper, which can lead to an increase in the current account deficit.
2. Decreased national savings: Government budget deficits are typically financed by borrowing, which can crowd out private investment and reduce national savings. Reduced national savings can lead to a lower level of domestic investment, limiting the productive capacity of the economy and potentially leading to a lower level of exports, thereby worsening the current account balance.
3. Increased interest rates: To finance a budget deficit, the government may need to borrow from the domestic market or international markets. This increased demand for funds can put upward pressure on interest rates. Higher interest rates can attract foreign capital inflows, increasing the demand for the domestic currency and exacerbating the current account deficit.
b. Given the following equations and values:
Y = C + I + G
Y = 5000
C(Y – T, r) = 1200 + 0.3(Y – T) – 50r
I(r) = 1500 – 50r
T = 1000
G = 1500
To find the equilibrium values of C, I, and r, we substitute the given values into the equations and solve for the unknowns.
From the first equation:
5000 = C + I + 1500
From the second equation:
C = 1200 + 0.3(5000 – 1000) – 50r
C = 1200 + 0.3(4000) – 50r
C = 1200 + 1200 – 50r
C = 2400 – 50r
From the third equation:
I = 1500 – 50r
Substituting these back into the first equation:
5000 = (2400 – 50r) + (1500 – 50r) + 1500
5000 = 2400 + 1500 + 1500 – 100r
100r = 5000 – 2400 – 1500 – 1500
100r = 300
r = 3
Therefore, the equilibrium values are:
C = 2400 – 50(3) = 2250
I = 1500 – 50(3) = 1350
r = 3
c. Now, if there is a technological innovation that makes businesses want to invest more, the investment equation becomes I(r) = 2000 – 50r.
Using the same process as before, we substitute this new equation into the first equation to find the new equilibrium values:
5000 = (2400 – 50r) + (2000 – 50r) + 1500
5000 = 2400 + 2000 + 1500 – 100r
100r = 5000 – 2400 – 2000 – 1500
100r = -900
r = -9
Therefore, the new equilibrium values are:
C = 2400 – 50(-9) = 2850
I = 2000 – 50(-9) = 2450
r = -9
d. To find the new values of private saving, public saving, and national saving, we can use the following equations:
Private saving (Sprivate) = Y – C – T
Public saving (Spublic) = T – G
National saving (Snational) = Sprivate + Spublic
Using the given values and the equilibrium values from part c:
Sprivate = 5000 – 2850 – 1000 = 1150
Spublic = 1000 – 1500 = -500
Snational = 1150 + (-500) = 650
Therefore, the new values of private saving, public saving, and national saving are:
Private saving = 1150
Public saving = -500
National saving = 650
a. Use the IS-LM & AD AS models to answer this question. Explain the effects of a decrease/ increase in price level on the economy
b. In terms of changing output, monetary policy is relatively more effective when the AS curve is horizontal, while fiscal policy is more effective when the AS curve is relatively vertical. Is this statement true or false? Justify your answer
c. When output deviates from the natural level of output, the economy is believed to "self-correct" over time. That is, the economy will return to the natural level of output without any policy intervention. explain how this process works
a. Decreasing the price level has different effects in the IS-LM and AD-AS models:
In the IS-LM model, a decrease in the price level leads to an increase in real money holdings (due to the nominal money supply remaining constant). This increase in real money balances lowers the interest rate, which stimulates investment and increases aggregate demand (AD), leading to an increase in output and income. Therefore, in the IS-LM model, a decrease in the price level leads to an expansionary effect on the economy.
In the AD-AS model, a decrease in the price level shifts the aggregate demand (AD) curve to the right. This is because a lower price level increases real wealth, which increases consumption expenditure, and also lowers the interest rate, which stimulates investment expenditure. However, the decrease in the price level also leads to a decrease in firms' revenues and profitability, causing a decrease in output. Therefore, in the AD-AS model, the effect of a decrease in the price level on the economy depends on other factors and may lead to a contractionary effect on output.
b. The statement is true.
Monetary policy is more effective when the AS (aggregate supply) curve is horizontal or nearly horizontal. A horizontal AS curve implies that changes in aggregate demand (AD) have a larger impact on output and a relatively smaller impact on the price level. In this situation, when the central bank conducts expansionary monetary policy and increases the money supply, it lowers interest rates, stimulates investment, and increases aggregate demand, which leads to a larger increase in output.
On the other hand, fiscal policy is more effective when the AS curve is relatively vertical or steep. A vertical AS curve implies that changes in aggregate demand have a larger impact on the price level and a relatively smaller impact on output. In this situation, when the government conducts expansionary fiscal policy by increasing government spending or reducing taxes, it directly increases aggregate demand, leading to a larger increase in the price level.
c. The process by which the economy self-corrects and returns to the natural level of output without policy intervention is known as the self-correcting mechanism or automatic stabilizers.
When output deviates from the natural level of output, it triggers forces that work to restore equilibrium. For example, if output is above the natural level, there may be an increase in inflationary pressures as demand outstrips supply. This may lead to higher wages and prices. Higher prices decrease real wages and decrease consumer purchasing power, which in turn reduces consumption expenditure. Additionally, higher prices incentivize firms to increase production, leading to an increase in supply. These adjustments help to bring the economy back toward the natural level of output.
Conversely, if output is below the natural level, there may be downward pressure on wages and prices as demand is weak relative to supply. Lower prices increase real wages and consumer purchasing power, stimulating consumption expenditure. Additionally, lower prices disincentivize firms from producing, leading to a decrease in supply. These adjustments help to bring the economy back toward the natural level of output.
The self-correction process takes time and is influenced by various factors, such as the flexibility of wages and prices, the speed of adjustment in the labor market, and the presence of structural barriers. Additionally, it assumes that there are no external shocks or disturbances that may disrupt the process.
a. In the model where it is assumed that the state of technology does not change, what parameters and/or variables cause changes in steady state output per worker.
b. Convergence refers to what phenomenon regarding growth theory?
c. Graphically illustrate and explain the effects of an increase in the saving rate on the Solow growth model. In your answer, you must clearly label all curves and the initial and final equilibria. In your answer, explain what happens to the rate of growth of output per worker and the rate of growth of output as the economy adjusts to this increase in the saving rate.
a. In the model where it is assumed that the state of technology does not change, changes in steady-state output per worker can be caused by changes in the following parameters and/or variables:
1. Savings rate (s): An increase in the savings rate leads to more investment, which increases the capital stock per worker in the long run. This, in turn, increases steady-state output per worker.
2. Depreciation rate (δ): A decrease in the depreciation rate reduces the rate at which capital stock per worker shrinks over time. With a lower depreciation rate, the capital stock per worker is higher in the long run, leading to higher steady-state output per worker.
3. Population growth rate (n): Higher population growth reduces the capital stock per worker, which in turn lowers steady-state output per worker.
4. Technological progress rate (A): If there is no technological progress, then changes in this parameter will not affect steady-state output per worker.
b. Convergence refers to the phenomenon in growth theory where economies with initially different levels of per capita income tend to converge towards similar levels of per capita income over time. This is often referred to as conditional convergence. The basic idea is that countries or regions that start with lower levels of income will have higher rates of economic growth, allowing them to catch up with countries or regions that start with higher levels of income.
c. In the Solow growth model, an increase in the saving rate (s) leads to higher investment, which increases the capital stock per worker. The effects of an increase in the saving rate can be shown graphically as follows:
- Label the horizontal axis as capital per worker (k) and the vertical axis as output per worker (y).
- Draw the production function curve, which begins to flatten as capital per worker increases due to diminishing returns to capital (label it as f(k)).
- Draw the depreciation curve (δk) which shows the rate at which capital per worker depreciates.
- Draw the investment curve (sy) which represents the new level of investment resulting from the increase in the saving rate.
- The initial equilibrium is where the investment curve intersects the 45-degree line (y = k) and the production function curve (f(k)). This represents the original steady state with a certain level of output per worker and capital per worker.
- With the increase in the saving rate, the investment curve shifts upwards.
- The new equilibrium is where the new investment curve intersects the production function curve and the 45-degree line. The capital per worker and output per worker are higher at this new steady state.
- The rate of growth of output per worker in the long run decreases as the economy approaches the new steady state. This is because the saving rate determines the rate at which capital per worker increases, and diminishing returns to capital result in diminishing increases in output per worker.
- The rate of growth of output in the economy also decreases as it approaches the new steady state, as the growth of population tends to reduce the per capita increase in output.
a. Explain what factors determine how much investment is required to maintain a given level of capital per effective worker.
b. Suppose an economy has a relatively low saving rate so that its steady state capital labor ratio is below its golden rule capital labor ratio.
i) Draw a graph to illustrate the concept of steady state. On your graph, show the golden rule capital labour ratio, output labour ratio.
ii) Suppose the government increased the saving rate to ensure enough investment to maintain the golden rule capital labor ratio as a steady state. Describe the transition of the economy from its initial steady state to the golden rule with the new higher saving rate.
a. The factors that determine how much investment is required to maintain a given level of capital per effective worker include the depreciation rate, the population growth rate, and the technological progress rate.
1. Depreciation rate (δ): This represents the rate at which capital stock wears out or depreciates over time. The higher the depreciation rate, the more investment is required to replace the depreciated capital and maintain a given level of capital per effective worker.
2. Population growth rate (n): This represents the rate at which the labor force grows. If the population growth rate is high, more investment is needed to provide capital for the growing labor force and maintain the capital per effective worker.
3. Technological progress rate (A): Technological progress increases labor productivity, allowing the same amount of capital to generate more output per worker. When technological progress is present, less investment is required to maintain a given level of capital per effective worker.
b.
i) To illustrate the concept of steady state, draw a graph with the capital per effective worker (k) on the horizontal axis and output per effective worker (y) on the vertical axis. On this graph, plot the steady-state capital labor ratio as a horizontal line, representing the level of capital per effective worker in the steady state. Plot the output labor ratio, which shows the level of output per effective worker achieved in the steady state.
ii) If the government increases the saving rate in an economy with a relatively low saving rate, it aims to ensure enough investment to maintain the golden rule capital labor ratio in the new steady state.
To describe the transition of the economy from its initial steady state to the golden rule with the higher saving rate:
1. Initially, the economy is in a steady state with a capital labor ratio below the golden rule. This means that the economy is not maximizing its long-run output per worker potential.
2. As the government increases the saving rate, it leads to higher investment. With increased investment, the capital per effective worker starts to increase over time.
3. Over the transition period, the economy experiences an increase in the capital per effective worker, leading to higher output per effective worker. As the capital labor ratio approaches the golden rule, the economy gets closer to its optimal long-run output per worker potential.
4. Once the new steady state is reached, the capital per effective worker stabilizes at the golden rule capital labor ratio. At this point, the economy is maximizing its long-run output per worker potential.
In summary, the increase in the saving rate leads to higher investment, which gradually increases the capital per effective worker and brings the economy closer to its
a. In solow growth model, explain what condition must occur for each of the following to occur: (1) the capital stock to increase; (2) the capital stock to decrease; and (3) the capital stock to remain constant.
b. Graphically illustrate and explain the effects of an increase in population growth on the Solow growth model. In your answer, you must clearly label all curves and the initial and final equilibria. In your answer, explain what happens to the rate of growth of output per worker and the rate of growth of output as the economy adjusts to this increase in population growth.