EBK MACROECONOMICS (FOURTH EDITION)
4th Edition
ISBN: 9780393616125
Author: Jones
Publisher: YUZU
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Chapter 7, Problem 8E
(a)
To determine
The formula for calculating the present discounted value today.
(b)
To determine
The formula for calculating the present discounted value today.
(c)
To determine
The value of a.
(d)
To determine
Calculate the present discounted value.
(e)
To determine
Explain the results of Part d.
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Consider the lifecycle model of labour supply with multiple periods. Assume
that the utility function in each period is the same thus preferences for
leisure and consumption are constant over time. Individuals aim to
maximise lifetime utility and are able to save and borrow. If individuals
know that the wage in period 1 (w1) will be lower than the wage in period 2
(w2), we expect that they will work [Select]
period 1 compared to period 2. This behaviour is called
[Select]
. Consumption is expected to be
hours in
[Select]
If individuals instead behave as if in a static labour supply model(*), faced
with the different wages in period 1 and 2 (w1
This is an extremely simple human capital accumulation problem. Let ht denote human capital of generation t (i.e., human capital of people born in year t). Suppose that human capital accumulates as a result of education spending, denoted by x and measured in 1,000 US dollars. If x = 30, the total spending is 30,000 US dollars and human capital of this individual is equal to ht = 2√x . Suppose that every individual has the same human capital, and output per individual is yt = Aht , where A > 0 is a fixed technology parameter. Find the (long-run) growth rate of yt . Show all your work, and interpret your results.
8. Valuing human capital with wage growth: To make the calculation of the present discounted value of a
worker's human capital more realistic, suppose labor income starts at $50,000 initially, but then grows at a
constant rate of 2% per year after that. Let w, be labor income in year t, so that
w; = Wo(1 +',
where wo = $50,000 and g= 0.02. The steps below will walk you through the problem.
1. If the interest rate is R, what is the formula for the present discounted value today (in year 0) of labor
income from a particular future year t?
2. Now add up these terms from t = 0 to = 45 to get a formula for the present discounted value of labor
income. Your answer should look something like that in equation (7.12).
3. Write your answer to part (b) so that it takes the form of the geometric series:
pdv = w.(1 + a + a? + a³ + .
+ at5).
What is the value of a that you find?
4. Apply the geometric series formula to compute the present discounted value for the case of R= 0.04, R
= 0.03, and R =…
Chapter 7 Solutions
EBK MACROECONOMICS (FOURTH EDITION)
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