Microeconomic Foundations: Consumption and Investment

Keynes and the consumption puzzle

Keynes built his consumption function on three conjectures:

1. $0 \lt MPC \lt 1$.
2. The average propensity to consume, $APC = C/Y$, falls as income rises: richer people save a larger fraction.
3. Current income is the main determinant of consumption.

Early household studies agreed: richer households consumed more (MPC > 0), saved more (MPC < 1) and saved a larger fraction of income (APC falls). Income and consumption were strongly correlated.

Then came the problem. If APC falls as income rises, then as countries grow richer, consumption should grow more slowly than income. Economists predicted exactly that after World War II. It did not happen. Simon Kuznets showed that the ratio $C/Y$ was very stable from decade to decade over long periods.

The life-cycle hypothesis

Franco Modigliani (1950s): income varies systematically over a person’s life, and people use saving to keep consumption smooth. The basic model assumes:

• initial wealth $W$, income $Y$ each year until retirement, $R$ years left until retirement and $T$ years left to live;
• a zero real interest rate, and smoothing consumption is optimal.

Lifetime resources are $W + RY$. Spread them evenly over $T$ years:

Solving the puzzle. Divide by $Y$: $APC = \alpha\,(W/Y) + \beta$.

• Across households, income varies more than wealth, so high-income households have a low $W/Y$ and a lower APC.
• Over time, aggregate wealth and income grow together, so $W/Y$ and the APC stay stable.

The theory also predicts that saving follows a pattern over life: positive while working, negative in retirement.

The permanent-income hypothesis

Milton Friedman (1957) splits current income into two parts:

Consumers smooth consumption through transitory changes by saving and borrowing. Consumption responds to permanent income.

Solving the puzzle. $APC = C/Y = \alpha Y^P/Y$.

• Across households, high-income households are more likely to have high transitory income that year, so their APC is lower.
• Over long periods, income changes are almost all permanent, so $Y^P/Y$ and the APC are stable.

Comparing the two. Both say people smooth consumption despite changing current income. In the life-cycle view, income changes systematically over life. In the permanent-income view, income has random, transitory fluctuations. Both explain the consumption puzzle.

The random-walk hypothesis

Robert Hall (1978) took the permanent-income hypothesis and added rational expectations: people use all available information to forecast their future income.

Then consumption should follow a random walk: changes in consumption should be unpredictable. Any change in income or wealth people could anticipate is already built into their permanent income, so it does not change consumption when it arrives. Only unanticipated news changes consumption.

The pull of instant gratification

The theories above assume perfectly rational lifetime utility maximisers. David Laibson and others study psychology. In one survey 76% of people said they were not saving enough for retirement.

Try the lecture’s two questions:

1. One candy today, or two candies tomorrow?
2. One candy in 100 days, or two candies in 101 days?

Most people choose the single candy today in question 1 and the two candies in question 2. But in 100 days, question 2 becomes question 1, and many would switch. That is time inconsistency: the pull of instant gratification explains why people save less than a fully rational planner would.

The lecture adds two more behavioural strands:

• Daniel Kahneman (Nobel 2002): the mind has a slow, deliberate pilot mode and a fast, emotional autopilot mode. Strong brands and habits work through autopilot.
• George Akerlof and Robert Shiller (Nobel 2001 and 2013): five animal spirits drive booms, recessions and crises: confidence, corruption, money illusion, fairness and stories.

Summing up consumption

Keynes: consumption depends mainly on current income. Later work: it also depends on expected future income, wealth and interest rates. Economists still disagree about the weight of these, of borrowing constraints (people who cannot borrow must consume out of current income, as Keynes assumed) and of psychology.

Investment

Three types:

• Business fixed investment: equipment and structures used in production.
• Residential investment: new housing, bought by occupants or landlords.
• Inventory investment: the change in stocks of finished goods, materials and work in progress.

The neoclassical model of business fixed investment

To separate decisions, imagine two kinds of firms: production firms rent capital to make goods, and rental firms own capital and rent it out. Investment is the rental firms’ spending on new capital.

• The real rental price of capital equals its marginal product: $R/P = MPK$ (from Lecture 3). It rises when capital is scarce, when employment rises or when technology improves.
• The cost of owning one unit of capital for a year is interest plus depreciation plus the capital loss (if the price of capital falls): $P_K\,(i - \Delta P_K/P_K + \delta)$. In real terms, approximately $\frac{P_K}{P}(r + \delta)$.
• The rental firm’s profit rate is $MPK - \frac{P_K}{P}(r + \delta)$.

So investment falls when the real interest rate rises, and rises when technology improves, when the capital stock is low relative to its steady state, or when the cost of capital falls.

Taxes

• Corporate income tax. In the economic definition of profit (rental price minus the true cost of capital) the tax would not affect investment. But the legal definition measures depreciation at the historical price of capital. When capital prices rise over time, that understates the true cost, overstates profit, and firms pay tax even when economic profit is zero. So the corporate tax discourages investment.
• Investment tax credit (ITC). Reduces a firm’s taxes for each lira spent on capital. It effectively lowers $P_K$, raises the profit rate and encourages investment.

Tobin’s q and the stock market

$q$ is the market value of installed capital divided by its replacement cost (Lecture 4). The $q$ theory and the neoclassical theory are closely related: $q$ is high when the stock market expects the future MPK of capital to exceed its cost.

A wave of pessimism about future profitability would lower stock prices, lower $q$, shift the investment function down and cause a negative demand shock. Falling stock prices also reduce household wealth and so consumption. And they may be a signal: bad news about technology and long-run growth means full-employment output will grow more slowly.

Summary and review

• Keynes: $0 \lt MPC \lt 1$, APC falls with income, current income matters most.
• Consumption puzzle: APC falls across households and in the short run, but is stable over long periods.
• Life cycle: $C = \alpha W + \beta Y$, $\alpha = 1/T$, $\beta = R/T$.
• Permanent income: $C = \alpha Y^P$; transitory income is mostly saved.
• Random walk: with rational expectations only surprises change consumption.
• Instant gratification: time inconsistency lowers saving.
• Investment rises with MPK, falls with $r$ and the cost of capital; corporate tax discourages it, ITC encourages it; $q$ links it to the stock market.