Question

1 Steady State and Covid-19 Shock In this section, suppose that productivity does not vary over time but is con- stant: A+ = A > O for all t. 1. Find the expression known as the law of motion of the equilibrium stock of capital. To this end, write down the market clearing condition of the capital market for period t +1 and substitute the expression that you found before for St+1. Use other equilibrium conditions (the equilibrium expression for wt) to get to an equation that gives Kt+1 as a function of Kt, and the parameters A, N,3,0,, a. 2. Represent graphically the Law of motion of capital (Kt+1 in the Y-axis and Kt in the X-axis. Indicate in the graph which is the steady state capital stock. 3. Assume that the economy is at the steady state equilibrium when it is unexpectedly affected by the Covid-19 shock. Since workers are sick, the disutility of working increases considerably which is reflected in an increase of o. Use the previous graph to explain the effects of this epidemic on the evolution of the capital stock in equilibrium. To this end, assume that in period to the capital stock is the steady state capital and o increases. Then, in the next period to +1 the disutility parameter o decreases to its initial value and remains at that level forever.

Answer 1

1. The law of motion tells you how capital per unit of effective labor evolves over time. In particular, it says that when actual investment (sk(t)α) is higher that required investment ((n + g + δ)k(t)), capital per unit of effective labor would be rising. Actual investment is the new investment in the economy.In economics, the Golden Rule savings rate is the rate of savings which maximizes steady state level or growth of consumption, as for example in the Solow growth model. ... A savings rate of 0% implies that no new investment capital is being created, so that the capital stock depreciates without replacement.Here capital markets to be "fully integrated" under the further condition that the ownership of capital is fully diversified. The model sketched in Figure 1 is deterministic, but we consider that an expository simplification of a model with uncertainty but no significant risk premia because of perfect diversification of capital ownership. Under this assumption, an increase in productivity in a region leads to an increase in output-Gross Domestic Product (GDP) or its regional counterpart-but is associated with a lower increase in income of the region-Gross National Income (GNI)

The general equilibrium model is static .Even when definced of T time periods the true flavour of dynamics of ongoing economy is missed .At the end of "I" period any stock left over with positive worth of the future generations.It follows the dynamic programming of the salvage value of left over stock, fails to capture some of the basic aspects of multigenerational economy.We would like to consider the implications of the overlap where several generatopms live overap has to take care of both young and old ones

c) Here since next period is t0+1

2. The law of motion tells you how capital per unit of effective labor evolves over time. In particular, it says that when actual investment (sk(t)α) is higher that required investment ((n + g + δ)k(t)), capital per unit of effective labor would be rising. Actual investment is the new investment in the economy.

Solow Model - An Overview Part 1 of many Therland M

When this happens, we've reached what is called the Steady-State Level of Capital. The steady-state is the key to understanding the Solow Model. At the steady-state, an investment is equal to depreciation. That means that all of investment is being used just to repair and replace the existing capital stock.Marginal product of capital (MPK) is the incremental increase in total production that results from one unit increase in capital while keeping all other inputs constant. α represents the proportion of capital and 1- α represents the proportion of labor required for production to occur and it includes both X axis as well as Y axis

3. As we write, the COVID-19 coronavirus is spreading throughout the globe. Besides its impact on public health, this coronavirus outbreak is likely to have significant economic consequences. The consensus is that the virus will cause a negative supply shock to the world economy, by forcing factories to shut down and disrupting global supply chains (OECD 2020).

The impact of coronavirus on aggregate demand

We take as our starting point a stripped-down version of the standard New Keynesian model (Gali 2009). As in the Keynesian tradition, employment and output are determined by aggregate demand. In turn, aggregate demand depends positively on productivity growth.  The reason for this is that faster productivity growth boosts agents’ expectations of future income, inducing them to spend more in the present (Lorenzoni 2009). This effect gives rise to a positive relationship between productivity growth (g) and employment (l), illustrated by the AD curve in Figure 1.

Figure 1 Impact of coronavirus on aggregate demand

Note: Employment on horizontal axis; productivity growth on vertical axis.

Imagine that the economy is initially at full employment (point (g,l ̅)). Then suppose that the coronavirus epidemic causes a persistent drop in productivity growth, from g to g'. As illustrated by the left panel of Figure 1, the result is lower demand and the emergence of involuntary unemployment (l < l ̅). The lesson is that the coronavirus epidemic, through its negative impact on agents’ expectations of future productivity growth, might induce a demand-driven recession.2

Now suppose that the central bank reacts by lowering the policy rate. This intervention sustains aggregate demand, by inducing agents to increase borrowing and spending. Graphically, this corresponds to a rightward shift of the AD curve to AD' If the monetary stimulus is strong enough, full employment is restored, as illustrated by the right panel of Figure 1. The model thus lends support to the idea that central banks might need to respond to the COVID-19 outbreak by easing monetary policy.3 Of course, this policy might conflict with the zero lower bound on interest rates. We will return to this point shortly.

The supply-demand doom loop

In reality, productivity growth is at least in part driven by firms’ investment. In turn, investment decisions depend on aggregate demand – when demand is strong, the return from investment tends to be high; weak aggregate demand, conversely, depresses firms’ incentives to invest. This effect gives rise to a positive relationship between productivity growth and aggregate demand, captured by the GG curve in Figure 2. The equilibrium is now determined by the intersection of two upward-sloping curves. This signals the presence of amplification effects.

Figure 2 The supply-demand doom loop

Let's again assume that the coronavirus spread generates a persistent negative supply shock, captured by a downward shift of the GG curve to GG'. What is interesting, is that now a supply-demand doom loop takes place. As before, the initial negative supply shock depresses aggregate demand. But now, lower demand induces firms to cut back on their investment, which generates an endogenous drop in productivity growth. Lower productivity growth, in turn, causes a further cut in demand, which again lowers productivity growth. This vicious spiral, or supply-demand doom loop, amplifies the impact of the initial supply shock on employment and productivity growth.

Now, monetary expansions have a multiplier effect on demand and employment. Suppose that the central bank eases monetary policy to increase aggregate demand. Higher demand, in turn, induces firms to increase investment. This sustains consumers’ expectations of future income, leading to a further rise in demand, and so on.  Monetary easing can thus reverse the supply-demand doom loop.