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Summary – Chapter 8
Private Sector Demand: Consumption and Investment
8.1 – Overview
- GDP represents the sum of all final goods expenditures
- Private consumption is a much more stable component over time than investment, which is volatile
and is often thought to be a major reason for business cycle fluctuations
- The consumption function is a symbolic way of stating that the aggregate consumption is positively
related to aggregate wealth, and if a significant proportion of households is constrained in credit
markets, to disposable income
- The investment function shows the relationship between investment and its fundamental
determinants: aggregate investment depends positively upon Tobin’s q and GDP growth, and
negatively upon the real interest rate
8.2 – Consumption
- The decision to consume is a decision not to save, and saving is a decision to postpone consumption
8.2.1 – Optimal Consumption
- Having access to a capital market allows people to borrow or lend: this is called intertemporal trade
- Consumer choices about consumption today and tomorrow depend on taste and preference which
is summarized by indifference curves
- Indifference curves are graphic representations of all possible combinations of two items that will
yield equivalent utility (satisfaction)
- Utility is the satisfaction that a consumer derives from the consumption of goods and services
- The higher the indifference curve, the higher the utility
- The slope of an indifference curve shows the willingness to switch between consumption today and
consumption tomorrow
- The curve of an indifference curve shows the willingness to substitute relative to the abundance of
consumption in the two periods
- The highest utility a consumer can reach is by choosing consumption on the indifference curve
which has a point tangent to the budget line
- A consumer who consumes on his budget line (spends his total wealth (OB)) will be shown like this:
𝐶2
𝑌2
𝐶1 +
= 𝑌1 +
= Ω
1+𝑟
1+𝑟
8.2.2 – Implications
Permanent versus temporary changes in income
Case 1: A temporary increase in income
- Experiencing a temporary increase in income, consumers will spend more today and save for later,
causing the budget line to have the same slope and shit outward
- That way, a temporary increase in income is accompanied by a permanent, but smaller, increase in
consumption
Case 2: A Permanent increase in income now and in the future
- Being equally better off in both periods, the consumer should see no reason for him to change his
spending pattern
- A permanent increase in income is absorbed in a permanent increase in consumption of similar size
Case 3: An expected future increase in income
- A consumer, knowing his income will increase in the future, will borrow more today in order to
increase his consumption in both periods
- However, changes in income are unpredictable in the future, and therefore changes in consumption
must be unpredictable, too
- The random walk theory of consumption describes a variable that changes randomly from period to
period, where the only change between its value today and its value tomorrow will be white noise
and can be positive or negative
Consumption smoothing
- People dislike variable consumption patterns
- Consumption smoothing describes the optimal choice by households to smooth out the impact of
temporary disturbances to income on consumption plans by either borrowing (in the case of a
negative shock) or saving (in the case of a positive shock)
- It is however very difficult to detect permanent from temporary shocks; consumers may be misled
by their perceptions
Permanent income and the life cycle
- The principle of optimal consumption implies that people should borrow when they are young and
repay debts and save when they are older in order to smooth the pattern of consumption over time
- Life-cycle consumption is a theory that consumption choices are made with a planning horizon
equal to the individual’s expected remaining lifetime; that an individual will build up savings during
working years and exhaust them during retirement years
- Permanent income is the flow of income which, if constant, would deliver the same present value
as the actual expected income path
- In the two period system, permanent income can be represented as:
𝑌𝑃
𝑌2
𝑃
𝑌 +
= 𝛺 = 𝑌1 +
1+𝑟
1+𝑟
Consumption and the real interest rate
- Increases in interest have important redistributive effects between borrowers and lenders: an
increase hurts the former and benefits the later
- An increase in the interest rate makes the budget constraint cheaper, therefore making it more
attractive to save today and consume tomorrow
- An increase in the interest rate also reduces the value of the present discounted value of all income.
The more wealth we have today, the more we profit from an increase in interest rates
8.2.3 – Wealth or Income?
- John Maynard Keynes argued that households simply set aside a fraction of disposable income for
saving, and consume the rest
- The link between consumption and disposable income is stronger than that between consumption
and wealth
- Wealth appears more volatile than disposable income, partly because of fluctuations in share prices
on the stock market
- Households are also not always able to borrow money from banks as they wish, because of the
riskiness of each customer. Some have to py higher interest rates than others, some have to give
securities
- Credit rationing is a condition in loan markets in which there is excess demand for loans at the
market interest rate
- In the presence of credit rationing, spending is governed by current disposable income, not wealth
- Even in developed countries, credit rationing affects a large proportion of households, therefore the
link between consumption and disposable income is seen as stronger
8.2.4 – The Consumption Function
- Consumption is driven by wealth, which in turn is based on current and future incomes of the
households
- The consumption function can be written in a compact way of linking consumption to its two main
determinants:
𝛺 𝑑
𝐶 = 𝐶( ,𝑌 )
+ +
- A high interest rate is bound to reduce consumption indirectly though wealth
8.3 – Investment
- Another component of aggregate demand is investment or gross capital formation
- The decision to invest is an intertemporal one, as investment goods are not intended for
consumption, but instead they make production of goods and services possible in the future
8.3.1 – The Optimal Capital Stock
- Marginal productivity of capital (MPK) is simply an additional output produced by employing an
additional unit of capital in the production process
- Through the principle of declining marginal productivity, the MPK declines as more and more capital
is put in place
- If an investment is funded with resources that could be investment in financial assets, the
opportunity cost of the investment is (1+r)
- Opportunity cost is the value of a resource in its best alternative use
- If an investment is financed by borrowing, the marginal cost of investment is (1+r)
- The firm’s profit in the second period is the difference between what it produces and the cost of
production
𝑃𝑟𝑜𝑓𝑖𝑡 = 𝐹(𝐾) − 𝐾(1 + 𝑟)
̅ , such that the distance between the
- To maximize profits, a firm chooses the optimal capital stock 𝐾
cost-of-capital schedule and the production function
- Optimal capital stock is the stock of physical capital that maximizes the value of the firm, for which
the marginal productivity of capital is equal to the marginal cost of investment
- The occurs where the slope of the production schedule is equal to the slope of the cost-of-capital
schedule:
𝑀𝑃𝐾
=
1+𝑟
Marginal
productivity
of capital
=
Marginal
cost of
capital
- Optimal capital stock depends positively on the expected effectiveness of the available technology,
which is shown by the marginal productivity of capital
- Optimal capital stock also depends negatively on the real interest rate
8.3.2 – Investment and the Real Interest Rate
- Investment occurs for two reasons: (1) to bring the capital stock to its desired level, and (2) to make
up for capital stock lost though physical or economic depreciation
̅− 𝐾
- Ignoring depreciation, optimal investment is simply the difference 𝐾
- An increase in the real interest rate lowers optimal stock of capital, and also lowers optimal
investment as the capital stock brought forward form the last period and the rate of depreciation
remain unchanged
- The investment function will be expressed as:
𝐼 = 𝐼(𝑟)
8.3.3 – The Accelerator Principle
- It is reasonable to expect that, for the capital stock to reach its optimal level, investment would
need to move in roughly the same proportion
- If the optimal capital stock in the second period is proportional to the expected output level: 𝐾 =
𝑣𝑌, where v is a constant, and an increase of GDP from 𝑌1 to 𝑌2 requires a change from 𝐾1 = 𝑣𝑌1 to
𝐾2 = 𝑣𝑌2 , then ignoring depreciation, this means an investment of:
𝐼1 = 𝐾2 − 𝐾1 = 𝑣(𝑌2 − 𝑌1 ) = 𝑣∆𝑌2
- This relationship shows the accelerator principle
- The accelerator principle is the positive effect of an increase in GDP on the rate of investment
- Increases in investment are associated with an acceleration of output
- Investment is more volatile than GDP as it is based on expectations of the future
8.3.4 – Investment and Tobin’s q
- Aggregate economic activity affects stock prices, and stock prices are important determinants of
aggregate economic activity
- The stock market valuation of a firm and its installed