Solution manual for advanced modern macroeconomics analysis and application 1st canadian edition by gillman

If the representative agent consumes goods c, according to the consumption function c= 1 1+a y P , where y P is permanent income, and α a constant parameter, then a an increase in perma

OF MACROECONOMICS

Max Gillman, Advanced Modern Macroeconomics, 1 Edition, Instructor’s Manual

Summary 1 Economic Way of Thinking – Model

Economists use models to study complicated economic phenomena They are like maps which only focus on the main streets of interest, ignoring details such as trees or stones In macroeconomic models, we focus on the main economic variables and relationships between them, e.g output, consumption, investment, capital and employment, ignoring other less important details Of course, the more details are included in the model, the more stylised facts can be explained There are two main sets of stylised facts to be explained by the models, i.e short run business cycles and long run trends including economic growth However, we never try to incorporate all the details in the model, because firstly we do not need them and secondly we cannot solve the model anyway Imagine how a map containing exactly the same information as the real world will be hard to read and have less value

Summary 2 Methodology of Modelling – Microfoundation

In modern macroeconomic models, the methodology of microfoundations, instead of ad hoc system of equations as adopted in traditional Keynesian models, is used In other words, the stylised facts in reality are explained altogether, rather than piece by piece It is done by deriving all the conditions in general equilibrium from well-defined microfounded problems It is just like when we draw a map we try to use a consistent measure to draw the whole map, rather than draw the map piece by piece using different measures

Summary 3 Logic of the Book

This book starts with the simplest model, with only one sector (goods sector) to explain some basic stylised facts of the real world Then the model is extended by including more details, i.e more sectors (human capital sector, banking sector, etc.) and policies (fiscal policy and monetary policy) This process is accumulative in the sense that the simpler model is just the special case of the more general model, treating some of the elements fixed Hence, anything that can be explained by the simple model can always be explained with modification by the more complicated model The flow chart illustrates the evolutionary path of the models

Stac Model without Growth (1-Sector)

Dynamic Model with Endogenous Growth (3-Sector)

Dynamic Model without Growth (1-Sector)

Dynamic Model with Exogenous Growth (1-Sector)

Dynamic Model with Endogenous Growth (2-Sector)

Dynamic Model with Endogenous Growth and Policies

Overview of the book

1 The microfoundations approach to macroeconomics stresses (a) the representative agent analysis;

(b) relative price analysis;

(c) AD−AS analysis;

(d) more than one of the above

2 From the general equilibrium economy, where there are 2 outputs, x and y, and a representative

consumer/producer, we can derive (a) the amount of goods ‘traded’ (the difference between consumption and production,

if any);

(b) the quantity supplied of x;

(c) the demand schedule for y;

(d) all of the above

3 If the representative agent consumes goods c, according to the consumption function

c= 1 1+a



y P , where y P is permanent income, and α a constant parameter, then

(a) an increase in permanent income raises consumption;

(b) an increase in the interest rate raises wealth;

(c) an increase in the real wage rate lowers consumption;

(d) all of the above

4 Suppose the consumption function is

c=

 1

1+ a



y P

where y P is permanent income and α a constant parameter Focusing on substitution and

income effects, indicate how to use this function to explain each of the following:

(a) business cycles;

(b) economic growth;

(c) old age pension insurance;

(d) the distribution of income

5 What are the main margins of economic analysis that make up the microfoundations approach

to macroeconomic analysis?

Max Gillman, Advanced Modern Macroeconomics, 1 Edition, Instructor’s Manual

6 What role does the capital stock play in forming the aggregate demand and supply analysis

in the dynamic model?

7 Define permanent income and explain how it affects the consumer’s demand for goods

8 Explain how the consumer’s demand for goods, or consumption function, changes as the economy goes from a static one to a dynamic one

9 Explain how aggregate demand is formed from the consumer’s demand for goods, in terms

of capital investment?

10 What role can comparative statics play in explaining business cycles and severe recessions?

11 What economic facts can be explained by the inclusion of human capital?

1.2 Answers

1 (d)

2 (d)

3 (a)

We have c= 1

1+αy P , so an increase in permanent income y P raises consumption c d (b) and

(c) are wrong because W t = w t T t

r −δ k + k t and y P = w t T t + ρk t

4 (a) Business cycles In the model with human capital, when human capital productivity shifts up, labour in the goods sector decreases as in a business cycle contraction, and time spent in the human capital sector increases as has been interpreting to occur when labour shifts from the market to the non-market sector in an contraction When human capital productivity falls, labour shifts back to the goods production sector, as the time endowment for labour and leisure is endogenously increased by the fall in human capital productivity

This gives the movement of labour as seen in the business cycle Combining the fall in human capital productivity with a rise in goods sector productivity, the wage rate indeed rises in an expansion In a contraction, a decrease in goods sector productivity combined with a rise in human capital sector productivity produces a decrease in the wage rate and in employment

in the goods sector According to c= 1

1+αy P, consumption will rise in expansion and fall in

contraction, because permanent income y Ppositively depends on wage and time endowment

(b) Economic growth The human capital feature that is crucial to this elemental business cycle explanation also explains important long term phenomena: the long secular fall in the labour workweek, the long secular increase in the time spent in education, and the long gradual increase in the worldwide growth rate These are all a direct result within the model

of the human capital sector productivity increasing very slightly, but steadily, over time

(c) Old age pension insurance According to the consumption function, consumption depends upon permanent income This illustrates the current-future consumption intertemporal choice

By consuming a fraction of permanent income, the consumer smooths the consumption across time To raise permanent income, the consumer needs to invest in both physical and human capital Basically, people save when they are young, and borrow when they are old, with the help of banking sector or government It is exactly the same mechanism of old age pension insurance

(d) The distribution of income A central question of economics is how to distributie income

in different dimensions so that consumption is smoothed This smoothing is the result of optimisation of a normally shaped utility function subject to the resource constraints For goods and leisure, this means that the consumer chooses a balance of goods consumption versus leisure, in the ‘intratemporal’ decision that allocates resources during the current time period For goods consumption across time, this means that the consumer chooses a balance of consumption today versus consumption tomorrow, in the ‘intertemporal’ decision that allocates resources across time periods The consumption function summarises the intratemporal and intertemporal conditions in the permanent income Also, if we have agents with different labour productivities or human capital levels, they will have different income levels

5 Hint: There are two basic types of margins to explain the behaviour of the representative agent Economic margins are simply the equilibrium conditions that describe the simultaneous balancing of the costs and benefits of alternatives during the period, across time and across

Max Gillman, Advanced Modern Macroeconomics, 1 Edition, Instructor’s Manual

states of nature The two primary margins are the marginal rate of substitution between goods and time (leisure) during the period and the marginal rate of substitution between goods, or time, over time or across states of nature The intratemporal goods-leisure margin links goods

to time during the period The intertemporal/interstate margin links the transfer of goods

or time across time or across states of nature to the investment set aside for such transfers during the current period Such investment is reaped only at a future time or a different state

of nature

6 Hint: In the dynamic model, the accumulation of capital links the periods over time and results in the intertemporal condition It creates a fundamental ‘state’ variable that must be

consistent with the AS −AD equilibrium; the AS−AD is written as a function of the state

variable, and it must be the correct value of the state variable

7 Hint: Permanent income is defined as a long run measurement of average income In

the static model, it is defined as wT +  In the dynamic model without human capital sector, it is defined as w t T t + ρ (1 + g) k t Here, the profit  on the fixed capital factor

becomes endogeneous rents to capital in the dynamic model In the dynamic model with

human capital sector, it is then defined as w t



1− g +δ h

A H



h t + ρ (1 + g) k t The consumption function suggests that the change in permanent income results in a proportional change in demand for goods

8 Hint: The fundamental change is the state variable capital stock In static model, consumption only depends on endowment in the same period In dynamic model, however, capital stock enables an intertemporal tradeoff between the present consumption and the future consumption

9 Hint: The aggregate demand AD for the output y t is equal to demand for goods plus investment With capital accumulation and zero growth, the investment demand is added to the consumption demand of equation With zero growth, investment need only cover the

depreciated capital, and so it equals δ k k t The AD function adds this δ k k t investment to the consumer demand for goods, to get:

y d t = c d

t + δ k k t = 1

1+ α (w t T t + [ρ + δ k (1+ α)] k t )

Similarly, in the model with exogenous growth, the capital income becomes k t ( t − δ k − g), instead of k t ( t − δ k )when there is zero growth The capital stock keeps growing, so that the

whole economy is in balanced growth path The new AD function becomes:

y d t = 1

1+ α (w t T t + k t [ρ (1 + g) + (δ k + g) (1 + α)])

In the model with endogenous growth, there are both physical capital and human capital

investment The time is now allocated among leisure, labour and education The AD function

becomes:

y d t = 1

1+ α



w t



1−g + δ h

A H



h t + k t [ρ (1 + g) + (δ k + g) (1 + α)]

.

10 Hint: Comparative statics on productivity changes are done by changing one exogenous parameter of the economy and finding the new equilibrium, and comparing it to the initial equilibrium before the parameter was changed

In the simple RBC model, as the productivity rises, the output expands, and so do consumption and investment On the contrary, when the productivity falls, the output declines, and the agent suffers low consumption and investment in the contraction However, labour does not have sufficient change, since time endowment is exogenously given, and there is no channel other than goods sector to allocate the time This problem is solved by including a human capital sector When the productivity in goods sector rises, the output of the goods sector expands as the human capital sector moves in the other direction Labour flows from the ‘non-market’ human capital sector to the goods sector, and this gives the central result

The employment rate rises in the goods sector In a decline of goods sector productivity, employment shifts towards the human capital sector, and the employment rate falls in the goods sector, this being a key fact of a business cycle contraction

A fixed wage rate is additionally allowed to show an occasional extreme decrease in employment, in both static and dynamic economies This is done by having the productivity decrease and the time decrease occur at the same time that the wage is fixed Then employment drops severely as in a depression, in a way to illustrate Keynes’s original ideas Instead of fixed prices, we can also explain the severe recessions by including banking sector The banking sector allows the economic choice of the transfer of goods, rather than time, over space, time, and states of nature under certain conditions The banking extension then again focuses on productivity changes, this time to the productivity of producing the intermediation service in the banking industry When, for example, there is a downwards drop in productivity

as in a banking crisis, then less savings is turned into investment, and consumption is not smoothed as well as otherwise

11 Hint: On the one hand, sufficient changes in the labour employment rate during the business cycle is explained by the inclusion of human capital It is accomplished by having a second production sector, the production of human capital investment, which endogenises the change

in time endowment On the other hand, the inclusion of human capital sector also allows the growth rate to be endogenous rather than being assumed as exogenous Goods sector productivity changes have no effect on the growth rate But changes in the human capital sector productivity do affect the growth rate of output This gives a fuller explanation of economic growth and, in particular, how tax distortions affect the output growth rate