Chapter 4 — Consumption and Investment Functions: Exercise Solutions Guide
How to Use This Page
1. Attempt every question on your own first — read the textbook chapter, then try the exercises without looking here. 2. Use this guide to verify your answers and understand the reasoning behind each one. 3. Practise all numerical problems — multiplier and propensity calculations are frequently asked in exams. 4. Memorise the key formulas (MPC, MPS, APC, APS, multiplier) and practise deriving one from another. 5. Revisit the "Common Mistakes" section before the exam to avoid frequent pitfalls.
Key Concepts (Quick Recap)
- Consumption function: C = a + bY, where C = consumption, a = autonomous consumption, b = MPC, Y = income.
- Marginal Propensity to Consume (MPC) = Delta-C / Delta-Y (fraction of additional income spent on consumption).
- Marginal Propensity to Save (MPS) = Delta-S / Delta-Y (fraction of additional income saved); MPC + MPS = 1.
- Average Propensity to Consume (APC) = C / Y; Average Propensity to Save (APS) = S / Y; APC + APS = 1.
- Savings function: S = −a + (1−b)Y, where S = savings, −a = dissaving at zero income, (1−b) = MPS.
- Investment multiplier: k = Delta-Y / Delta-I = 1/(1 − MPC) = 1/MPS.
- Autonomous investment: Independent of income (e.g., government spending on infrastructure).
- Induced investment: Depends on income and profit expectations (rises with income).
- Keynes's psychological law of consumption: Men are disposed to increase their consumption as income increases, but not by as much as the increase in income (MPC > 0 but MPC < 1).
I. Choose the Best Answer (MCQs)
1. The consumption function is expressed as: (a) C = a − bY (b) C = a + bY (c) C = b − aY (d) C = a + Y/b
Answer(b) C = a + bY — The Keynesian consumption function shows that consumption (C) equals autonomous consumption (a) plus the product of MPC (b) and income (Y).
2. If MPC = 0.75, then MPS equals: (a) 0.75 (b) 0.25 (c) 1.75 (d) 1.25
Answer(b) 0.25 — Since MPC + MPS = 1, MPS = 1 − 0.75 = 0.25.
3. The investment multiplier is calculated as: (a) k = MPC (b) k = 1/MPC (c) k = 1/(1 − MPC) (d) k = 1 − MPC
Answer(c) k = 1/(1 − MPC) — The multiplier shows the ratio of change in income to change in investment. Since MPC + MPS = 1, k = 1/MPS as well.
4. If MPC = 0.6 and investment increases by Rs. 200, the increase in income will be: (a) Rs. 200 (b) Rs. 300 (c) Rs. 500 (d) Rs. 120
Answer(c) Rs. 500 — k = 1/(1 − 0.6) = 1/0.4 = 2.5. Delta-Y = k x Delta-I = 2.5 x 200 = Rs. 500.
5. Autonomous consumption refers to: (a) Consumption that depends on income (b) Consumption that does not depend on income (c) Consumption that equals savings (d) Consumption that equals investment
Answer(b) Consumption that does not depend on income — Autonomous consumption (a) is the minimum level of consumption even when income is zero, financed by past savings or borrowing.
6. Keynes's psychological law of consumption states that: (a) MPC = 0 (b) MPC = 1 (c) 0 < MPC < 1 (d) MPC > 1
Answer(c) 0 < MPC < 1 — Keynes's law states that as income increases, consumption also increases but by less than the increase in income. Therefore, MPC is positive but less than 1.
7. The savings function is expressed as: (a) S = a + bY (b) S = −a + (1 − b)Y (c) S = a − bY (d) S = b + aY
Answer(b) S = −a + (1 − b)Y — When income is zero, savings are negative (−a = dissaving). As income rises, savings increase at the rate of MPS (1 − b).
8. APC stands for: (a) Average Propensity to Consume (b) Absolute Propensity to Consume (c) Additional Propensity to Consume (d) Autonomous Propensity to Consume
Answer(a) Average Propensity to Consume — APC = C / Y, the ratio of total consumption to total income.
9. Which of the following is true about the multiplier? (a) Higher MPC leads to a lower multiplier (b) Higher MPC leads to a higher multiplier (c) Multiplier is independent of MPC (d) Multiplier equals MPC
Answer(b) Higher MPC leads to a higher multiplier — Since k = 1/(1 − MPC), as MPC increases, (1 − MPC) decreases, and k increases. For example, MPC = 0.5 gives k = 2; MPC = 0.8 gives k = 5.
10. Induced investment depends on: (a) Government policy only (b) Income level and profit expectations (c) Nothing — it is constant (d) Only the interest rate
Answer(b) Income level and profit expectations — Induced investment varies with the level of income and the expected rate of return. It rises when income rises and falls when income falls.
II. Fill in the Blanks
1. The consumption function is expressed as C = a + bY.
2. MPC + MPS = 1.
3. The investment multiplier k = 1 / (1 − MPC) = 1 / MPS.
4. APC + APS = 1.
5. When income is zero, consumption equals autonomous consumption (a) and savings are negative (−a) (dissaving).
6. MPS = 1 − MPC.
7. Keynes's psychological law states that as income increases, consumption increases but by less than the increase in income.
8. Autonomous investment is independent of changes in income.
9. Induced investment varies with the level of income and profit expectations.
10. The value of the multiplier is inversely related to MPS (higher MPS means lower multiplier).
III. True or False
1. MPC can be greater than 1. False. — MPC is the fraction of additional income spent on consumption. It cannot exceed 1 because one cannot spend more than the additional income received. Keynes's law states 0 < MPC < 1.
2. APC can be greater than 1 at low levels of income. True. — At very low income levels, consumption may exceed income (people borrow or use past savings), making APC = C/Y greater than 1.
3. The multiplier is higher when MPC is lower. False. — The multiplier k = 1/(1 − MPC). A higher MPC gives a higher multiplier, not a lower one. If MPC = 0.8, k = 5; if MPC = 0.5, k = 2.
4. Saving is a leakage from the circular flow of income. True. — Saving reduces the amount of income that flows back as consumption expenditure, creating a leakage. Investment is the corresponding injection.
5. Autonomous consumption is zero when income is zero. False. — Autonomous consumption (a) is positive even when income is zero. People must consume to survive, so they dissave (borrow or use past savings) to maintain a minimum level of consumption.
6. The multiplier works in both directions — for increases and decreases in investment. True. — Just as an increase in investment causes a multiplied increase in income, a decrease in investment causes a multiplied decrease in income.
7. APC is always less than MPC. False. — At low income levels, APC > MPC because the autonomous consumption component makes average consumption higher. As income rises, APC falls and approaches MPC.
8. Induced investment is independent of the level of income. False. — Induced investment depends on the level of income and profit expectations. It is autonomous investment that is independent of income.
IV. Match the Following
| Column A | Column B |
|---|
| 1. MPC | (a) C / Y |
| 2. MPS | (b) Delta-C / Delta-Y |
| 3. APC | (c) Delta-S / Delta-Y |
| 4. APS | (d) S / Y |
| 5. Multiplier (k) | (e) 1 / (1 − MPC) |
| 6. Consumption function | (f) S = −a + (1−b)Y |
| 7. Savings function | (g) C = a + bY |
Answer1 — (b) MPC = Delta-C / Delta-Y (Marginal Propensity to Consume). 2 — (c) MPS = Delta-S / Delta-Y (Marginal Propensity to Save). 3 — (a) APC = C / Y (Average Propensity to Consume). 4 — (d) APS = S / Y (Average Propensity to Save). 5 — (e) k = 1 / (1 − MPC). 6 — (g) Consumption function: C = a + bY. 7 — (f) Savings function: S = −a + (1−b)Y.
V. Answer Briefly
1. Define the consumption function.
Answer
The consumption function, introduced by Keynes, shows the functional relationship between total consumption and total income. It is expressed as C = a + bY, where C is total consumption, a is autonomous consumption (consumption at zero income), b is the marginal propensity to consume (MPC), and Y is income. The consumption function is upward-sloping, indicating that consumption increases as income increases, but by less than the increase in income.
2. What is the marginal propensity to consume (MPC)?
Answer
The Marginal Propensity to Consume (MPC) is the ratio of the change in consumption to the change in income that caused it. MPC = Delta-C / Delta-Y. It measures the proportion of each additional unit of income that is spent on consumption. For example, if income increases by Rs. 100 and consumption increases by Rs. 80, then MPC = 80/100 = 0.8. According to Keynes, 0 < MPC < 1.
3. What is the average propensity to consume (APC)?
Answer
The Average Propensity to Consume (APC) is the ratio of total consumption to total income: APC = C / Y. It shows the proportion of total income that is spent on consumption. For example, if C = Rs. 800 and Y = Rs. 1,000, then APC = 800/1000 = 0.8. At low income levels, APC can exceed 1 (when people consume more than they earn by borrowing).
4. Distinguish between APC and MPC.
Answer
| Basis | APC (Average Propensity to Consume) | MPC (Marginal Propensity to Consume) | |---|---|---| | Formula | C / Y | Delta-C / Delta-Y | | Meaning | Ratio of total consumption to total income | Ratio of change in consumption to change in income | | Value at zero income | Undefined (Y = 0) | Positive (autonomous consumption exists) | | Trend | Falls as income rises | Relatively stable | | Relationship | APC > MPC at low income levels | Can be less than APC |
5. What is Keynes's psychological law of consumption?
Answer
Keynes's psychological law of consumption states three propositions: 1. When income increases, consumption also increases, but by a smaller amount (MPC > 0). 2. The increased income is distributed between consumption and saving (MPC < 1). 3. The increase in income always leads to an increase in both consumption and saving (MPC + MPS = 1). In essence: as income rises, people spend more, but they save an increasing proportion of the additional income.
6. What is the investment multiplier? State its formula.
Answer
The investment multiplier (k) measures the magnified effect of a change in investment on national income. It is the ratio of the change in income to the change in investment: k = Delta-Y / Delta-I. Since the multiplier depends on how much of additional income is spent, k = 1/(1 − MPC) = 1/MPS. For example, if MPC = 0.8, then k = 1/(1 − 0.8) = 1/0.2 = 5. This means a Rs. 100 increase in investment will increase national income by Rs. 500.
7. Distinguish between autonomous and induced investment.
Answer
| Basis | Autonomous Investment | Induced Investment | |---|---|---| | Definition | Independent of income level | Depends on income and profit expectations | | Motive | Social welfare, public goods | Profit motive | | Made by | Government | Private firms | | Changes with income | Does not change | Increases with income | | Examples | Infrastructure, defence | Factory expansion, new machinery | | Curve | Horizontal (parallel to X-axis) | Upward-sloping (rises with income) |
VI. Answer in Detail
1. Explain Keynes's consumption function with a diagram description and numerical example.
Answer
Keynes's consumption function shows the relationship between consumption and income: C = a + bY. Components: - a = Autonomous consumption: The minimum level of consumption that exists even when income is zero. People must eat, clothe themselves, and find shelter, so they borrow or use past savings to maintain this consumption. - b = MPC (Marginal Propensity to Consume): The slope of the consumption function, showing how much consumption increases for each unit increase in income. - Y = Income: The independent variable that determines consumption. Key Properties: 1. The consumption function is upward-sloping: as income increases, consumption increases. 2. The slope of the consumption function (MPC) is less than 1: consumption increases by less than the increase in income. 3. The consumption function starts above the origin (at point a on the Y-axis) because of autonomous consumption. 4. At low income levels, consumption exceeds income (dissaving). The break-even point is where C = Y (the 45-degree line intersects the consumption function). Numerical Example: | Income (Y) | Consumption (C = 50 + 0.8Y) | Saving (S = Y − C) | |---|---|---| | 0 | 50 | −50 | | 100 | 130 | −30 | | 200 | 210 | −10 | | 250 | 250 | 0 | | 300 | 290 | 10 | | 400 | 370 | 30 | | 500 | 450 | 50 | At Y = 250, C = 250 (break-even point). Below this, the household dissaves; above this, it saves. Diagram Description: The consumption function is drawn as an upward-sloping line starting at point a (autonomous consumption) on the vertical axis. The 45-degree line from the origin represents Y = C. The break-even point is where the consumption function intersects the 45-degree line.
2. Explain the investment multiplier with its working process.
Answer
The investment multiplier (k) explains how an initial increase in investment leads to a multiplied increase in national income through successive rounds of consumption spending. Formula: k = Delta-Y / Delta-I = 1/(1 − MPC) = 1/MPS Working Process: Suppose the government increases investment by Rs. 1,000 crore and MPC = 0.8. | Round | Increase in Income | Increase in Consumption (MPC = 0.8) | Increase in Saving (MPS = 0.2) | |---|---|---|---| | 1st (Investment) | 1,000 | 800 | 200 | | 2nd | 800 | 640 | 160 | | 3rd | 640 | 512 | 128 | | 4th | 512 | 409.6 | 102.4 | | ... | ... | ... | ... | | Total | 5,000 | 4,000 | 1,000 | Verification: k = 1/(1 − 0.8) = 1/0.2 = 5. Delta-Y = k x Delta-I = 5 x 1,000 = Rs. 5,000 crore. Logic: In the first round, the Rs. 1,000 investment becomes income for someone. That person spends 80% (MPC = 0.8) = Rs. 800 on consumption. This Rs. 800 becomes income for another person, who spends 80% = Rs. 640, and so on. The process continues until the leakage through saving (MPS = 0.2) exhausts the multiplier effect. Conditions for the Multiplier to Work: 1. MPC must be greater than zero (there must be some consumption spending). 2. There must be unemployed resources so that output can expand. 3. There should be no supply bottlenecks. 4. The increased demand must be met by increased production. Reverse Multiplier: The multiplier also works in reverse. A decrease in investment causes a multiplied decrease in income. If investment falls by Rs. 1,000 crore, income falls by Rs. 5,000 crore (with MPC = 0.8).
3. Explain the relationship between consumption and saving functions.
Answer
Consumption and saving are complementary functions — they are two parts of how income is used. Fundamental Identity: Y = C + S (Income = Consumption + Saving) From this: - S = Y − C (Saving = Income − Consumption) - APC + APS = 1 (C/Y + S/Y = 1) - MPC + MPS = 1 (Delta-C/Delta-Y + Delta-S/Delta-Y = 1) Consumption Function: C = a + bY Savings Function: S = −a + (1 − b)Y Key Relationships: 1. When income is zero, consumption is a (autonomous) and saving is −a (dissaving). The household borrows or uses past savings. 2. At the break-even point, C = Y and S = 0. All income is consumed, none is saved. 3. Below the break-even point, C > Y and S < 0 (dissaving). 4. Above the break-even point, C < Y and S > 0 (positive saving). 5. The slope of the consumption function is MPC (b); the slope of the savings function is MPS (1 − b). 6. When MPC rises, MPS falls, and vice versa. Diagram Description: When the consumption function and savings function are drawn on the same graph with income on the X-axis: - The consumption function starts above the origin at point a. - The savings function starts below the origin at point −a. - At the break-even income, the consumption function intersects the 45-degree line (C = Y), and the savings function crosses the X-axis (S = 0). - Above the break-even point, the gap between the 45-degree line and the consumption function equals positive saving.
4. Explain the determinants of investment.
Answer
Investment refers to expenditure on capital goods that yield income in the future. The two main determinants are: 1. Marginal Efficiency of Capital (MEC): The MEC is the expected rate of return on an additional unit of capital. It depends on: - Prospective yield: The expected future income from the capital asset. - Supply price (replacement cost): The cost of acquiring the capital asset. - MEC = (Prospective yield − Supply price) / Supply price - A firm will invest if MEC > rate of interest. As more investment occurs, MEC falls (due to diminishing returns), and investment stops when MEC = rate of interest. 2. Rate of Interest: The rate of interest is the cost of borrowing funds for investment. Investment is profitable only if the expected return (MEC) exceeds the cost of borrowing (interest rate). - If MEC > interest rate, investment is profitable → investment increases. - If MEC < interest rate, investment is unprofitable → investment decreases. - The investment demand schedule (MEC schedule) slopes downward: as the interest rate falls, more investment projects become viable. Other Determinants: 3. Business expectations: Optimism about future demand increases investment; pessimism reduces it. 4. Level of income: Higher income creates higher demand, inducing more investment. 5. Government policy: Tax incentives, subsidies, and low interest rates encourage investment. 6. Technological progress: New technologies create new investment opportunities. 7. Political stability and institutional framework: Uncertainty discourages long-term investment. Autonomous vs. Induced Investment: - Autonomous investment is independent of income (e.g., government infrastructure spending). - Induced investment depends on income and profit expectations and is represented by an upward-sloping curve.
Common Mistakes to Avoid
1. Using MPC instead of (1 − MPC) in the multiplier formula — k = 1/(1 − MPC), NOT 1/MPC. If MPC = 0.8, k = 1/0.2 = 5, not 1/0.8 = 1.25.
2. Confusing APC and MPC — APC = C/Y (average); MPC = Delta-C/Delta-Y (marginal). APC can exceed 1 at low incomes; MPC is always between 0 and 1.
3. Forgetting that MPC + MPS = 1 — If MPC = 0.75, then MPS = 0.25, NOT some other value. This identity always holds.
4. Confusing autonomous and induced investment — Autonomous investment is constant regardless of income (horizontal line); induced investment rises with income (upward-sloping line).
5. Saying "saving is always positive" — At income levels below the break-even point, saving is negative (dissaving). Only above the break-even point is saving positive.
6. Applying the multiplier when there is full employment — The investment multiplier works only when there are unemployed resources. At full employment, additional demand causes inflation, not increased output.
Exam Checklist
- [ ] I can write and explain the consumption function (C = a + bY)
- [ ] I can calculate MPC, MPS, APC, APS from given data
- [ ] I can state and apply the multiplier formula (k = 1/(1 − MPC) = 1/MPS)
- [ ] I can solve numerical problems on the multiplier (given MPC and Delta-I, find Delta-Y)
- [ ] I can explain the working of the multiplier through successive rounds
- [ ] I can distinguish between autonomous and induced investment
- [ ] I can explain Keynes's psychological law of consumption
- [ ] I can derive the savings function from the consumption function and explain their relationship
