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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,...
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,...
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,...
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...
Assume the representative consumer lives in two periods and his preferences can be described by the...
Assume the representative consumer lives in two periods and his preferences can be described by the utility function U(c; c') = c1/3 + B(c')1/3; where c is the current consumption, c' is next period consumption, and B = 0.95. Let's assume that the consumer can borrow or lend at the interest rate r = 10%. The consumer receives an income y = 100 in the current period and y' = 110 in the next period. The government wants to spend...
Consider the Solow growth model. Output at time t is given by the production function Yt...
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...
2. TIME PREFERENCE In class, we solved a two-period savings model where a consumer allocates income...
2. TIME PREFERENCE In class, we solved a two-period savings model where a consumer allocates income across two periods. We assumed the consumer’s intertemporal utility function was given by: U(c1,c2) = log(c1) + δlog(c2) and that their intertemporal budget constraint was M1 + M2 = c1 + c2 . 1+r 1+r Along the way to solving that problem, we found that consumers should select their consumption in each period so that: u′(c1) = δ(1 + r)u′(c2), where δ is the...
Consider the Solow growth model. Output at time t is given by the production function Y-AK3...
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...
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...
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...
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...
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 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...
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