BECC-109 Solved Assignment

INTERMEDIATE MACROECONOMICS-II

Assignment I

1. State the basic assumptions of the Solow model. Derive the condition for steady state level of capital stock in an economy.
2. Explain how an economy converges to a steady state growth path in the Romer model of endogenous growth.

Assignment II

3. Discuss the important features and various phases of business cycles.
4. Explain how the multiplier and the accelerator interact to generate business cycles.
5. Describe how the permanent income hypothesis attempts to resolve the Kuznets’ puzzle on consumption function.

Assignment III

6. Explain the concept of loss function. How does the shape of the function change according to perception of inflation and unemployment by the Central Bank?
7. State the major inferences on policy that we can draw on the basis of new-classical economics.
8. Describe the various channels of monetary transmission mechanism.
9. Discuss the implications of portfolio balance approach to risk and return.
10. Write a short note on the characteristics of residential investment.

Expert Answer

State the basic assumptions of the Solow model. Derive the condition for steady state level of capital stock in an economy.

Answer:

• Production Function: The model assumes a Cobb-Douglas production function, $Y=F(K,L)$$Y=F(K,L)$Y=F(K,L)Y = F(K, L)$Y=F(K,L)$, where $Y$$Y$YY$Y$ is output, $K$$K$KK$K$ is capital, and $L$$L$LL$L$ is labor. The production function exhibits constant returns to scale, meaning that if both capital and labor are scaled by the same factor, output will increase by that factor.
• Diminishing Returns to Capital and Labor: The model assumes diminishing marginal returns to both capital and labor, meaning that as more capital or labor is added, the additional output generated from each additional unit decreases.
• Exogenous Technological Progress: Technological progress, denoted by $A$$A$AA$A$, is considered exogenous, meaning it occurs independently of the economy’s internal dynamics. The model assumes that technology improves at a constant rate over time, contributing to long-term growth.
• Savings Rate: A constant fraction of output is saved and invested in capital accumulation. The savings rate, denoted by $s$$s$ss$s$, is exogenous and does not change over time.
• Population Growth: The labor force grows at a constant rate $n$$n$nn$n$. The model assumes that population growth is exogenous and does not influence capital accumulation directly.
• Capital Depreciation: Capital depreciates at a constant rate $\delta$$\delta$delta\delta$\delta$, meaning that a certain fraction of the capital stock wears out and needs to be replaced each period.

• Investment: In the Solow model, investment is the portion of output saved and allocated to increasing the capital stock. It is represented as $I=sY$$I=sY$I=sYI = sY$I=sY$, where $I$$I$II$I$ is investment and $s$$s$ss$s$ is the savings rate.
• Depreciation: Capital depreciates at a constant rate $\delta$$\delta$delta\delta$\delta$, reducing the capital stock over time. The total depreciation in the economy is given by $\delta K$$\delta K$delta K\delta K$\delta K$.
• Net Capital Accumulation: The net change in the capital stock is the difference between investment and depreciation. This is represented by the equation:
  $$\mathrm{\Delta }K=sY-\delta K$$$$\mathrm{\Delta }K=sY-\delta K$$Delta K=sY-delta K\Delta K = sY – \delta K$$\mathrm{\Delta }K=sY-\delta K$$
  where $\mathrm{\Delta }K$$\mathrm{\Delta }K$Delta K\Delta K$\mathrm{\Delta }K$ is the change in the capital stock.

• Condition for Steady State: The steady state is achieved when the net change in capital accumulation ($\mathrm{\Delta }K$$\mathrm{\Delta }K$Delta K\Delta K$\mathrm{\Delta }K$) is zero, meaning that investment equals depreciation:
  $$sY=\delta K$$$$sY=\delta K$$sY=delta KsY = \delta K$$sY=\delta K$$
  At this point, the capital stock remains constant, and the economy grows at the rate of technological progress and population growth.
• Deriving the Steady State Condition: To derive the steady state level of capital, we substitute the production function $Y=F(K,L)$$Y=F(K,L)$Y=F(K,L)Y = F(K, L)$Y=F(K,L)$ into the condition for steady state:
  $$sF(K,L)=\delta K$$$$sF(K,L)=\delta K$$sF(K,L)=delta KsF(K, L) = \delta K$$sF(K,L)=\delta K$$
  Assuming a Cobb-Douglas production function $F(K,L)=K^{\alpha }{L}^{1-\alpha }$$F(K,L)=K^{\alpha }{L}^{1-\alpha }$F(K,L)=K^( alpha)L^(1-alpha)F(K, L) = K^\alpha L^{1-\alpha}$F(K,L)=K^{\alpha }{L}^{1-\alpha }$, where $\alpha$$\alpha$alpha\alpha$\alpha$ is the capital share of output, we have:
  $$s{K}^{\alpha }{L}^{1-\alpha }=\delta K$$$$s{K}^{\alpha }{L}^{1-\alpha }=\delta K$$sK^( alpha)L^(1-alpha)=delta KsK^\alpha L^{1-\alpha} = \delta K$$s{K}^{\alpha }{L}^{1-\alpha }=\delta K$$
  Dividing both sides by $K$$K$KK$K$ and solving for $K$$K$KK$K$, we get the steady state level of capital per worker, $k^{\ast }$$k^{\ast }$k^(**)k^*$k^{\ast }$:
  $$k^{\ast }={\left(\frac{s}{\delta +n+g}\right)}^{\frac{1}{1-\alpha }}$$$$k^{\ast }={\left(\frac{s}{\delta +n+g}\right)}^{\frac{1}{1-\alpha }}$$k^(**)=((s)/(delta+n+g))^((1)/(1-alpha))k^* = \left(\frac{s}{\delta + n + g}\right)^{\frac{1}{1-\alpha}}$$k^{\ast }={\left(\frac{s}{\delta +n+g}\right)}^{\frac{1}{1-\alpha }}$$
  where $k^{\ast }=\frac{K}{L}$$k^{\ast }=\frac{K}{L}$k^(**)=(K)/(L)k^* = \frac{K}{L}$k^{\ast }=\frac{K}{L}$ is the steady state capital per worker, $n$$n$nn$n$ is the population growth rate, and $g$$g$gg$g$ is the rate of technological progress.

• No Long-Term Growth from Capital Accumulation: In the steady state, capital accumulation alone does not lead to long-term economic growth. Once the economy reaches the steady state, any further increases in capital are offset by depreciation and population growth.
• Role of Technological Progress: Long-term economic growth in the Solow model is driven by technological progress, which shifts the production function upward and allows for sustained increases in output per worker, even in the steady state.
• Convergence: The Solow model predicts that economies with similar savings rates, population growth rates, and technology levels will converge to the same steady state level of output per worker over time. This implies that poorer economies will grow faster than richer ones until they catch up, assuming similar fundamental parameters.

Explain how an economy converges to a steady state growth path in the Romer model of endogenous growth.

Answer:

• Endogenous Technological Change: Technological progress is the result of intentional activities such as research and development (R&D). The model assumes that firms invest in R&D to create new knowledge, which in turn drives productivity and economic growth.
• Nonrivalry of Knowledge: Knowledge is considered a nonrival good, meaning that one firm’s use of knowledge does not diminish its availability to others. This assumption leads to increasing returns to scale in knowledge production.
• Positive Externalities: Knowledge created by one firm can spill over to others, generating positive externalities that benefit the entire economy. These spillovers are a key source of sustained growth in the Romer model.
• Human Capital: The model assumes that human capital is essential for producing new knowledge. A larger pool of skilled workers increases the economy’s capacity for innovation and knowledge creation.

• Production Function: The output $Y$$Y$YY$Y$ in the economy is given by:
  $$Y=A\cdot K^{\alpha }\cdot L^{1-\alpha }$$$$Y=A\cdot K^{\alpha }\cdot L^{1-\alpha }$$Y=A*K^( alpha)*L^(1-alpha)Y = A \cdot K^\alpha \cdot L^{1-\alpha}$$Y=A\cdot K^{\alpha }\cdot L^{1-\alpha }$$
  where $A$$A$AA$A$ represents the stock of knowledge, $K$$K$KK$K$ is capital, $L$$L$LL$L$ is labor, and $\alpha$$\alpha$alpha\alpha$\alpha$ is the output elasticity of capital.
• Knowledge Accumulation: Knowledge $A$$A$AA$A$ accumulates over time as firms invest in R&D. The rate of knowledge accumulation is given by:
  $$\dot{A}=\delta H\cdot A$$$$\dot{A}=\delta H\cdot A$$A^(˙)=delta H*A\dot{A} = \delta H \cdot A$$\dot{A}=\delta H\cdot A$$
  where $\dot{A}$$\dot{A}$A^(˙)\dot{A}$\dot{A}$ is the rate of change of knowledge, $\delta$$\delta$delta\delta$\delta$ is the productivity of R&D, and $H$$H$HH$H$ represents human capital employed in knowledge production.
• Positive Feedback Loop: As knowledge accumulates, it increases the productivity of labor and capital, leading to higher output. Higher output, in turn, allows for greater investment in R&D, creating a positive feedback loop that sustains growth.

• Initial Divergence and Transition Dynamics: In the short run, economies with different initial levels of knowledge and human capital may experience divergent growth rates. However, as knowledge accumulates and positive externalities from knowledge spillovers become more pronounced, these differences diminish over time.
• Balancing Knowledge Accumulation and Depreciation: The economy reaches a steady state growth path when the rate of knowledge accumulation balances with the effective depreciation of knowledge. In this context, depreciation refers to the diminishing marginal returns to additional knowledge creation. The steady state is characterized by a constant growth rate of knowledge and, consequently, a constant growth rate of output.
• Role of Human Capital and R&D Investment: The steady state growth path depends on the sustained investment in human capital and R&D. Economies that invest more in education, training, and innovation will converge to a higher steady state growth rate. Conversely, economies with lower levels of investment may converge to a lower growth path.
• Endogenous Growth Rate: Unlike exogenous models like Solow, where the long-term growth rate is determined by external factors, the Romer model allows the economy’s growth rate to be influenced by policy decisions, institutional factors, and other endogenous variables. This makes the steady state growth rate flexible and responsive to changes in the economic environment.

• Policy Interventions: Government policies that promote education, innovation, and R&D can accelerate the convergence process by enhancing the economy’s capacity for knowledge creation and utilization.
• Institutional Quality: Strong institutions that protect intellectual property rights, enforce contracts, and support innovation can foster a conducive environment for sustained growth and quicker convergence.
• Initial Conditions: The initial level of human capital and knowledge stock plays a critical role in determining the speed and direction of convergence. Economies with higher initial levels of these factors may converge more rapidly to their steady state growth paths.
• International Knowledge Spillovers: In a globalized economy, international trade and collaboration can facilitate the diffusion of knowledge across borders, allowing economies to benefit from advancements made elsewhere and converge to higher growth paths.

Discuss the important features and various phases of business cycles.

Answer:

• Recurring Nature: Business cycles are recurrent but not periodic, meaning they occur repeatedly over time but do not follow a fixed schedule.
• Comprehensive Impact: Business cycles affect all sectors of the economy, including production, employment, income, and consumption.
• Asymmetry: The duration and intensity of expansions and contractions can vary significantly, with expansions often lasting longer than contractions.
• Self-Reinforcing: During expansion phases, positive feedback loops, such as increased consumer spending and investment, amplify economic growth. Conversely, during contractions, negative feedback loops can deepen the downturn.

• Expansion: This phase is characterized by increasing economic activity. Key indicators such as GDP, employment, and consumer spending rise. Businesses invest more, consumer confidence improves, and unemployment falls. This phase continues until the economy reaches its peak.
• Peak: The peak represents the highest point of economic activity before a downturn begins. At this stage, economic indicators are at their highest levels, but growth starts to slow as the economy overheats.
• Contraction (Recession): During contraction, economic activity begins to decline. Indicators like GDP, employment, and spending decrease. Businesses may cut back on investment, unemployment rises, and consumer confidence weakens. A severe contraction can lead to a recession.
• Trough: The trough is the lowest point of economic activity in the cycle. It marks the end of the contraction phase and the beginning of a new expansion. Economic indicators stop declining and start to stabilize.

Explain how the multiplier and the accelerator interact to generate business cycles.

Answer:

Describe how the permanent income hypothesis attempts to resolve the Kuznets’ puzzle on consumption function.

Answer:

Explain the concept of loss function. How does the shape of the function change according to perception of inflation and unemployment by the Central Bank?

Answer:

State the major inferences on policy that we can draw on the basis of new-classical economics.

Answer:

Describe the various channels of monetary transmission mechanism.

Answer:

1. Interest Rate Channel: Central banks influence short-term interest rates, which affect borrowing and spending by households and businesses, thereby impacting aggregate demand.
2. Credit Channel: Changes in monetary policy affect the availability of credit by influencing banks’ lending capacity and the cost of credit.
3. Exchange Rate Channel: Monetary policy can influence exchange rates, affecting export and import prices, thus impacting net exports and aggregate demand.
4. Asset Price Channel: Changes in policy rates influence asset prices (e.g., stocks, bonds), which affect wealth and consumer spending.
5. Expectations Channel: Policy signals affect expectations about future economic conditions, influencing spending and investment decisions.

Discuss the implications of portfolio balance approach to risk and return.

Answer:

1. Diversification: Investors diversify their portfolios to minimize risk without sacrificing expected returns. By holding a mix of assets with low or negative correlations, the overall portfolio risk is reduced.
2. Risk-Return Trade-off: Investors choose a portfolio that balances their desired level of return with their willingness to accept risk. Higher returns generally require taking on more risk.
3. Market Impact: Central banks and policymakers can influence asset prices and yields by altering the supply of different assets, affecting investors’ portfolio choices and the broader economy.

Write a short note on the characteristics of residential investment.

Answer:

1. Cyclical Nature: Residential investment is highly sensitive to economic cycles, often expanding during economic booms and contracting during downturns.
2. Interest Rate Sensitivity: It is particularly responsive to changes in interest rates, as lower rates reduce the cost of borrowing for homebuyers and investors, thereby stimulating demand.
3. Long-Term Commitment: Residential investment typically involves long-term financial commitments, such as mortgages, making it a significant decision for households.
4. Multiplier Effect: It has a strong multiplier effect on the economy, influencing related industries like construction, manufacturing, and real estate services.