II) A consumer behavior is described by the equation Y1 = C4 + Se where Yt,...
II) A consumer behavior is described by the equation Yt = Ct + St where Yt, Ct and St stand respectively for the income, consumption and saving of the consumer at the time period t. We assume that Ct = {Yt+1 – 7 and St = 53 Y+ at any time period t. 1. Write down the difference equation of consumption of the consumer. 2 marks For the subsequent questions, we assume that the consumption of the consumer satisfies the...
II) A consumer behavior is described by the equation Yt = C+ + St where Yt, Ct and St stand respectively for the income, consumption and saving of the consumer at the time period t. We assume that Ct = {Y{+1 – 7 and S4 = 55 Y4 at any time period t. 1. Write down the difference equation of consumption of the consumer. 2 marks For the subsequent questions, we assume that the consumption of the consumer satisfies the...
II) A consumer behavior is described by the equation Y4 = C+ + S where Y, Ct and S stand respectively for the income, consumption and saving of the consumer at the time period t. We assume that Ct = {Y{+1 – 7 and S = 3 Y at any time period t. 1. Write down the difference equation of consumption of the consumer. 2 marks For the subsequent questions, we assume that the consumption of the consumer satisfies the...
Consider the Solow growth model. Output at time t is given by the production function Yt = AK 1 3 t L 2 3 where Kt is total capital at time t, L is the labour force and A is total factor productivity. The labour force and total factor productivity are constant over time and capital evolves according the transition equation Kt+1 = (1 − d) ∗ Kt + It , where d is the depreciation rate. Every person saves...
Consider the Solow growth model. Output at time t is given by the production function Y-AK3 Lš where K, is total capital at time t, L is the labour force and A is total factor productivity. The labour force and total factor productivity are constant over time and capital evolves according the transition equation KH = (1-d) * Kit It: where d is the depreciation rate. Every person saves share s of his income and, therefore, aggregate saving is St-s...
1. (45 points) Consider the closed-economy one-period macroeconomic model developed in class. The consumer is endowed with h units of time, and chooses consumption C and leisure ` to maximize U = log(C) + θlog(`), subject to the budget constraint C = wNs + π. Production is described by Y = zNd . Government spending G is financed with a proportional revenue tax (tax rate τ ) on the firm. (a) (10) Find the firm’s optimal demand for labor Nd...
The following problem is based on the idea of a Malthusian trap. Thomas Malthus, an 18th century British cleric and scholar, argued that as population increases, the limited amount of natural resources will lead societies into a trap of gradually decreasing standard of living, thus negating the effects of any technological progress. We can study this idea using the Solow model framework. Consider a modified version of the Solow growth model where the aggregate production function in period t is...
3. The Consumer Price Index (CPI) represents the average price of goods that households consume. Many thousands of goods are included in such an index. Here consumers are repre- sented as buying only food (pizza) and gas as their basket of goods. Below is a representation of the kind of data the Bureau of Economic Analysis (BEA) collects to construct a consumer price index. In the base year, 2008, both the prices of goods purchased and the quantity of goods...
Just 5-8
1 Analytics of the Solow Model In the Solow economy, people consume a good that firms produce with technology Y (which we assume to be constant) and f is a Cobb-Douglas production function Af (K, L), where A is TFP f(K, L) KL-a Here K is the stock of capital, which depreciates at rate δ E (0, 1) per period, and L is the labor force, which grows exogenously at rate n > 0. Here employment is always...
Please help solve this, using the equation
to get through the problem.
Additional information:
where the initial position
, the initial speed
The above differential equation can also be written as:
If
, there is light damping where the solution has the form ( where r
and w are two positive constants)
or
If
there is heavy damping where,
where
and
are two positive constants
If
there is critical damping where,
where r is a positive constant
d'y dy ma...