06/06/2026, 16:16 Consumption & Investment Theory — Revision Guide
ECON2291 · LEVEL 2 ECONOMIC THEORY · REVISION GUIDE
The Microfoundations of
Consumption and Investment
Complete theory, formal derivations, past paper answers and practice questions
CONTENTS
1. The Keynesian Consumption Function
2. The Fisher Intertemporal Model
3. Life-Cycle Hypothesis (Modigliani)
4. Permanent Income Hypothesis (Friedman)
5. Random Walk Hypothesis (Hall)
6. Ricardian Equivalence
7. Behavioural Departures and Empirical Evidence
8. Neoclassical Model of Investment
9. Tobin's q
10. Financing Constraints
11. Past Paper and Specimen Questions with Model Answers
12. Practice Questions
13. Key References
1. The Keynesian Consumption Function
Keynes's General Theory (1936) offered the first systematic account of aggregate
↑
consumption. His model was built on three conjectures, each with testable
file:///C:/Users/tyala/Downloads/consumption_investment_revision_guide (1).html#pastpapers 1/32
,06/06/2026, 16:16 Consumption & Investment Theory — Revision Guide
implications.
The Three Keynesian Conjectures
CONJECTURE 1 — MARGINAL PROPENSITY TO CONSUME
When income rises, consumption rises by a fraction of that increase. Formally,
0 < MPC < 1 , where MPC = dC/dY.
CONJECTURE 2 — FALLING AVERAGE PROPENSITY TO CONSUME
The ratio of consumption to income, APC = C/Y, falls as income rises. Keynes
argued that saving was a luxury good accessible primarily to the wealthy.
CONJECTURE 3 — CURRENT INCOME PRIMACY
Current income, not wealth or the interest rate, is the principal determinant
of consumption.
These conjectures are captured in the linear consumption function:
KEYNESIAN CONSUMPTION FUNCTION
C = C̄ + cY, C̄ > 0, 0 < c < 1
where C̄ is autonomous consumption and c is the MPC. The APC = C/Y = C̄ /Y + c,
which falls as Y rises, satisfying Conjecture 2.
The Consumption Puzzle
Early cross-sectional studies (e.g. Brady and Friedman, 1947) and short time-series
supported the Keynesian function, finding a positive relationship between current
income and consumption with a declining APC. However, Simon Kuznets (1946)
examined long-run time-series data and found that the saving rate remained
roughly constant over time, implying a constant APC rather than a falling one. This
↑
contradiction is sometimes called the consumption puzzle. It motivated
file:///C:/Users/tyala/Downloads/consumption_investment_revision_guide (1).html#pastpapers 2/32
,06/06/2026, 16:16 Consumption & Investment Theory — Revision Guide
Modigliani's life-cycle hypothesis and Friedman's permanent income hypothesis,
both of which resolve the apparent inconsistency.
The core insight driving post-Keynesian theories is that consumers are forward-looking. They
smooth consumption over time, so spending depends not on current income alone but on
lifetime resources and expectations.
2. The Fisher Intertemporal Model
Fisher (1930) provided the microeconomic foundations for intertemporal
consumption choice. Consider a consumer who lives for two periods, receiving
income y_t in period t and y_{t+1} in period t+1, facing real interest rate r.
Deriving the Lifetime Budget Constraint
In period t, the consumer's flow constraint is:
c_t + s_t = y_t
In period t+1, savings earn interest, so:
c_{t+1} = s_t(1 + r) + y_{t+1}
Solving for s_t from the second equation and substituting into the first gives the
lifetime budget constraint:
LIFETIME BUDGET CONSTRAINT (FISHER)
c_t + c_{t+1}/(1 + r) = y_t + y_{t+1}/(1 + r)
The left side is the present value of consumption; the right side is the present value
↑
of lifetime income (human wealth). The slope of the budget constraint is -(1 + r) ,
file:///C:/Users/tyala/Downloads/consumption_investment_revision_guide (1).html#pastpapers 3/32
, 06/06/2026, 16:16 Consumption & Investment Theory — Revision Guide
reflecting the market trade-off: consuming one extra unit today costs (1 + r)
units of future consumption.
The Utility Maximisation Problem
The consumer maximises lifetime utility, discounting future utility at rate β ∈
(0,1) (the subjective discount factor):
OBJECTIVE FUNCTION
max U = u(c_t) + β·u(c_{t+1}) subject to: c_t + c_{t+1}/(1 + r) =
y_t + y_{t+1}/(1 + r)
Deriving the Euler Equation
DERIVATION — EULER EQUATION
1. Form the Lagrangian: L = u(c_t) + β·u(c_{t+1}) + λ[y_t + y_{t+1}/(1+r) − c_t −
c_{t+1}/(1+r)]
2. First-order condition with respect to c_t: ∂L/∂c_t = u′(c_t) − λ = 0, so λ = u′
(c_t)
3. First-order condition with respect to c_{t+1}: ∂L/∂c_{t+1} = β·u′(c_{t+1}) −
λ/(1+r) = 0, so λ = β(1+r)u′(c_{t+1})
4. Equating the two expressions for λ yields the Euler equation.
EULER EQUATION
u′(c_t) = β(1 + r)·u′(c_{t+1}) Equivalently: u′(c_t) / [β·u′
(c_{t+1})] = (1 + r) MRS between periods = MRT between periods
Interpreting the Euler Equation
The Euler equation equates the marginal rate of substitution (MRS) between ↑
present and future consumption to the market rate of return (1 + r) . It describes
file:///C:/Users/tyala/Downloads/consumption_investment_revision_guide (1).html#pastpapers 4/32
ECON2291 · LEVEL 2 ECONOMIC THEORY · REVISION GUIDE
The Microfoundations of
Consumption and Investment
Complete theory, formal derivations, past paper answers and practice questions
CONTENTS
1. The Keynesian Consumption Function
2. The Fisher Intertemporal Model
3. Life-Cycle Hypothesis (Modigliani)
4. Permanent Income Hypothesis (Friedman)
5. Random Walk Hypothesis (Hall)
6. Ricardian Equivalence
7. Behavioural Departures and Empirical Evidence
8. Neoclassical Model of Investment
9. Tobin's q
10. Financing Constraints
11. Past Paper and Specimen Questions with Model Answers
12. Practice Questions
13. Key References
1. The Keynesian Consumption Function
Keynes's General Theory (1936) offered the first systematic account of aggregate
↑
consumption. His model was built on three conjectures, each with testable
file:///C:/Users/tyala/Downloads/consumption_investment_revision_guide (1).html#pastpapers 1/32
,06/06/2026, 16:16 Consumption & Investment Theory — Revision Guide
implications.
The Three Keynesian Conjectures
CONJECTURE 1 — MARGINAL PROPENSITY TO CONSUME
When income rises, consumption rises by a fraction of that increase. Formally,
0 < MPC < 1 , where MPC = dC/dY.
CONJECTURE 2 — FALLING AVERAGE PROPENSITY TO CONSUME
The ratio of consumption to income, APC = C/Y, falls as income rises. Keynes
argued that saving was a luxury good accessible primarily to the wealthy.
CONJECTURE 3 — CURRENT INCOME PRIMACY
Current income, not wealth or the interest rate, is the principal determinant
of consumption.
These conjectures are captured in the linear consumption function:
KEYNESIAN CONSUMPTION FUNCTION
C = C̄ + cY, C̄ > 0, 0 < c < 1
where C̄ is autonomous consumption and c is the MPC. The APC = C/Y = C̄ /Y + c,
which falls as Y rises, satisfying Conjecture 2.
The Consumption Puzzle
Early cross-sectional studies (e.g. Brady and Friedman, 1947) and short time-series
supported the Keynesian function, finding a positive relationship between current
income and consumption with a declining APC. However, Simon Kuznets (1946)
examined long-run time-series data and found that the saving rate remained
roughly constant over time, implying a constant APC rather than a falling one. This
↑
contradiction is sometimes called the consumption puzzle. It motivated
file:///C:/Users/tyala/Downloads/consumption_investment_revision_guide (1).html#pastpapers 2/32
,06/06/2026, 16:16 Consumption & Investment Theory — Revision Guide
Modigliani's life-cycle hypothesis and Friedman's permanent income hypothesis,
both of which resolve the apparent inconsistency.
The core insight driving post-Keynesian theories is that consumers are forward-looking. They
smooth consumption over time, so spending depends not on current income alone but on
lifetime resources and expectations.
2. The Fisher Intertemporal Model
Fisher (1930) provided the microeconomic foundations for intertemporal
consumption choice. Consider a consumer who lives for two periods, receiving
income y_t in period t and y_{t+1} in period t+1, facing real interest rate r.
Deriving the Lifetime Budget Constraint
In period t, the consumer's flow constraint is:
c_t + s_t = y_t
In period t+1, savings earn interest, so:
c_{t+1} = s_t(1 + r) + y_{t+1}
Solving for s_t from the second equation and substituting into the first gives the
lifetime budget constraint:
LIFETIME BUDGET CONSTRAINT (FISHER)
c_t + c_{t+1}/(1 + r) = y_t + y_{t+1}/(1 + r)
The left side is the present value of consumption; the right side is the present value
↑
of lifetime income (human wealth). The slope of the budget constraint is -(1 + r) ,
file:///C:/Users/tyala/Downloads/consumption_investment_revision_guide (1).html#pastpapers 3/32
, 06/06/2026, 16:16 Consumption & Investment Theory — Revision Guide
reflecting the market trade-off: consuming one extra unit today costs (1 + r)
units of future consumption.
The Utility Maximisation Problem
The consumer maximises lifetime utility, discounting future utility at rate β ∈
(0,1) (the subjective discount factor):
OBJECTIVE FUNCTION
max U = u(c_t) + β·u(c_{t+1}) subject to: c_t + c_{t+1}/(1 + r) =
y_t + y_{t+1}/(1 + r)
Deriving the Euler Equation
DERIVATION — EULER EQUATION
1. Form the Lagrangian: L = u(c_t) + β·u(c_{t+1}) + λ[y_t + y_{t+1}/(1+r) − c_t −
c_{t+1}/(1+r)]
2. First-order condition with respect to c_t: ∂L/∂c_t = u′(c_t) − λ = 0, so λ = u′
(c_t)
3. First-order condition with respect to c_{t+1}: ∂L/∂c_{t+1} = β·u′(c_{t+1}) −
λ/(1+r) = 0, so λ = β(1+r)u′(c_{t+1})
4. Equating the two expressions for λ yields the Euler equation.
EULER EQUATION
u′(c_t) = β(1 + r)·u′(c_{t+1}) Equivalently: u′(c_t) / [β·u′
(c_{t+1})] = (1 + r) MRS between periods = MRT between periods
Interpreting the Euler Equation
The Euler equation equates the marginal rate of substitution (MRS) between ↑
present and future consumption to the market rate of return (1 + r) . It describes
file:///C:/Users/tyala/Downloads/consumption_investment_revision_guide (1).html#pastpapers 4/32
