Table 1.1.6. Real Gross Domestic Product, Chained Dollars Download UPDATED

Table 1.1.6. Real Gross Domestic Product, Chained Dollars Download

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Question 1 (12 points)

1. (a)  Write down the Euler equation for the two-period consumption-saving trouble in full general terms (as derived in class) and describe its economic intuition.
2. (b)  Consider the Euler equation for the two-period consumption-saving trouble. Suppose β(1 + rt) < i. Is the growth rate of consumption positive, negative, or aught? Explicate.
3. (c)  Graphically draw the solution to the consumption-saving problem. Clearly state why you know it is the solution.

Question two (16 points)

Consider the post-obit consumption-savings problem. The consumer solves max Cα+βCα

Ct ,Ct+1 ,St t t+1 bailiwick to the lifetime budget constraint

Ct+ Ct+1 =Yt+ Yt+1 1+rt one+rt

where we assume that β ∈ (0,i) and α > 0.

1. (a)  Nether which assumption on α are marginal utilities from consumption positive simply diminishing?
2. (b)  Derive the Euler equation from the household's constrained maximization problem.
3. (c)  Using the Euler equation and the lifetime budget constraint, solve for the period t consumption office (i.e. Ct∗).
4. (d)  What happens to the household's optimal consumption in flow t when β increases? Provide some intuition.

Question iii (15 points)

Suppose that a household only lives for i menses. The household's optimization problem is:

max U=lnCt+θtln(one−Nt) Ct ,Nt

bailiwick to

Ct = wtNt + Yt
where Nt denotes labor supply, Ct denotes consumption, wt is the wage rate, and Yt is

exogenous non-labor income. θ > 0 is a parameter.

1. (a)  Solve for the household'due south optimal labor supply and consumption.
2. (b)  What can yous say about the upshot of wt on the optimal Nt? Provide some economic intuition.
3. (c)  What tin you say most the effect of Yt on the optimal Nt? Provide some economic intuition.

Question iv (fifteen points)

Consider the following data for average hours of piece of work per week across countries.

Figure 1: Average hours of piece of work per week beyond countries. Source: Bick et al. (2018). Reproduced from Kurlat (2020).

Presume we want to write down a model of household labor supply that allows us to under- stand this design. To do then, nosotros assume that household preferences are given past:

u(c, l) = ln(c) + θl

where c is consumption, 50 is leisure and θ is a parameter. Households have a total of one unit of fourth dimension available and tin supply labor at a wage rate w. Notation that the household budget constraint is then given past c = w · (one − fifty).

1. (a)  Discover an expression for the fraction of their fourth dimension that households optimally spend in market place work.
2. (b)  If this was the right model and one looked at households in different countries, how would hours of work correlate with wage levels?
3. (c)  Because the empirical bear witness above, do you remember this is a skillful model of house- agree labor supply?

Question 5 (xviii points)

Suppose these are the prices (in Usa dollars) and quantities of goods A and B produced in the The states in 2017 and 2018:

pA qA atomic number 82 qB 2017 4 5 iii 3 2018 i ten iv 2

1. (a)  Compute nominal GDP in 2017.
2. (b)  Compute nominal GDP in 2018.
3. (c)  What was real GDP in 2018 at 2017 prices (computed using stock-still 2017 prices)? Using this measure, how much did GDP abound between 2017 and 2018?
4. (d)  What was real Gdp in 2017 at 2018 prices (computed using fixed 2018 prices)? Using this mensurate, how much did GDP abound betwixt 2017 and 2018?
5. (eastward)  Why is at that place a deviation betwixt your answer in (c) compared to (d)?
6. (f)  Statisticians utilise a technique called 'concatenation-weighting' in club to avoid the bug arising from different base of operations years. It works as follows
   1. (a)  Summate real Gdp at 2017 prices.
   2. (b)  Summate real GDP at 2018 prices.
   3. (c)  Calculate growth rate of real GDP between 2017 and 2018 using both base of operations years and take the geometric average of the two growth rates. [Hint: The geometric

√

average of a and b is given by:
How much did Gross domestic product grow between 2017 and 2018 using the chain-weighted method?

Question half dozen (24 points)

[Excel Problem] Download quarterly, seasonal adjusted data on US real GDP, personal consumption expenditures, and gross private domestic investment for the period 1960Q1- 2021Q4. You tin discover these data in the BEA NIPA Table 1.ane.6, "Real Gross Domestic Product, Chained Dollars".

(a) c

ab.]

2. (b)  The growth rate of a random variable x, betwixt dates t − 1 and t is defined as 1000 tx = ten t − x t − 1 xt−one Calculate the growth rate of each of the 3 serial (using the raw serial, not the logged serial) and write down the average growth charge per unit of each series over the entire sample menstruum. Are the average growth rates of each series approximately the aforementioned?
3. (c)  The standard deviation of a series of random variables is a measure of how much the variable jumps around about its mean ("=stdev(serial)"). Take the time series standard deviations of the growth rates of the iii series mentioned above and rank them in terms of magnitude.
4. (d)  In this subquestion we try to go a sense of the cost of the COVID-nineteen recession that started in 2020Q1. Compute the average growth charge per unit of real GDP for the period 2015Q1-2019Q4. Compute a counterfactual time path of the level of real GDP if information technology had grown at that charge per unit between 2020Q1 and 2021Q4. Visually compare that counterfactual fourth dimension path of Gdp to bodily Gdp, and come up with a rough guess of the cost of the COVID-nineteen recession (in dollars).

References

[one] Alexander Bick, Nicola Fuchs-Schu ̈ndeln, and David Lagakos. How do hours worked vary with income? cross-country show and implications. American Economic Review, 108(1):170–99, 2018.

[two] Pablo Kurlat. A Course in Modernistic Macroeconomics. 2020.

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