Consumer Behaviour: Utility, Marginal Utility, Budget Constraint & Choice

Key Concepts and Definitions

Utility and Marginal Utility

Utility is the satisfaction or happiness a consumer derives from consuming goods and services. It is a subjective measure and varies from person to person.

Marginal Utility (MU) is the additional satisfaction gained from consuming one more unit of a good or service. It is calculated as the change in total utility divided by the change in quantity consumed.

Law of Diminishing Marginal Utility: As a consumer consumes more units of a good, the additional satisfaction (marginal utility) derived from each additional unit tends to decrease.

Cardinal vs. Ordinal Utility

• Cardinal Utility: Measures utility in absolute numerical terms (e.g., 10 utils for one apple, 20 utils for two apples). This approach is criticized for being subjective and difficult to quantify.
• Ordinal Utility: Ranks preferences without assigning numerical values (e.g., "I prefer A over B"). This is the basis of indifference curve analysis (covered in Unit 5).

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Budget Constraint and Consumer Choice

Budget Line

A budget line (or budget constraint) shows all combinations of two goods that a consumer can afford given their income and the prices of the goods. It is defined by the equation:

$$P_{x}X+P_{y}Y=M$$

Where:

• $P_x$ = Price of good X
• $P_y$ = Price of good Y
• $X$ = Quantity of good X
• $Y$ = Quantity of good Y
• $M$ = Total income (budget)

The slope of the budget line is given by: $$\text{Slope}=-\frac{P_x}{P_y}$$

```figure
{"type":"curves","lines":[{"label":"Budget Line","from":[0,10],"to":[10,0],"expr":"y = (-Px/Py)*x + (M/Py)"}],"points":[{"x":0,"y":10,"label":"Intercept Y","xmark":"M/Py","ymark":""},{"x":10,"y":0,"label":"Intercept X","xmark":"","ymark":"M/Px"}],"xlabel":"Quantity of Good X","ylabel":"Quantity of Good Y","caption":"Budget line for goods X and Y with intercepts at M/Px and M/Py, slope = -Px/Py (M=1000, Px=100, Py=50)"}

### Consumer Equilibrium
A consumer is in equilibrium when they maximize their utility given their budget constraint. This occurs when:
1. The budget is fully spent (no unused income).
2. The marginal utility per rupee spent on each good is equal:
   $$\frac{M{U}_x}{P_x}=\frac{M{U}_y}{P_y}$$

```figure
{"type":"curves","lines":[{"label":"Indifference Curve (IC1)","from":[1,9],"to":[9,1],"expr":"y = -x + 10"},{"label":"Budget Line","from":[0,10],"to":[10,0],"expr":"y = -x + 10"}],"points":[{"x":5,"y":5,"label":"Consumer Equilibrium","xmark":"X*","ymark":"Y*"}],"xlabel":"Good X","ylabel":"Good Y","caption":"Consumer equilibrium where budget line is tangent to indifference curve"}

This is known as the Equi-Marginal Principle.

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Worked Example: Choosing Between Tea and Coffee

Scenario: Suppose a student has a budget of Rs. 200 per week. The price of tea is Rs. 20 per cup, and the price of coffee is Rs. 10 per cup. The student’s marginal utility (MU) for tea and coffee is given below:

Step 1: Determine the Budget Line

• Maximum tea: $\frac{200}{20}=10$ cups.
• Maximum coffee: $\frac{200}{10}=20$ cups.
• Budget line equation: $20X+10Y=200$ or $2X+Y=20$.

Step 2: Find the Optimal Combination We need to find $X$ and $Y$ such that: $$\frac{M{U}_x}{P_x}=\frac{M{U}_y}{P_y}$$ $$\frac{M{U}_x}{20}=\frac{M{U}_y}{10}$$ $$M{U}_x=2\times M{U}_y$$

Let’s test combinations:

• For $X=2$, $M{U}_x=40$. Then $M{U}_y=20$. From the table, $M{U}_y=20$ when $Y=3$. Check budget: $2(2)+3=7\ne 20$. Not feasible.
• For $X=3$, $M{U}_x=30$. Then $M{U}_y=15$. From the table, $M{U}_y=15$ when $Y=4$. Check budget: $2(3)+4=10\ne 20$. Not feasible.
• For $X=4$, $M{U}_x=20$. Then $M{U}_y=10$. From the table, $M{U}_y=10$ when $Y=5$. Check budget: $2(4)+5=13\ne 20$. Not feasible.

Correction: We need to find a combination where the budget is fully spent. Let’s try $X=4$ and $Y=12$:

• Budget check: $2(4)+12=20$. Feasible.
• $M{U}_x=20$, $M{U}_y=15$ (for $Y=4$, but $Y=12$ is beyond the table). This suggests we need to interpolate or adjust.

Alternative Approach: Use the budget line to find feasible combinations and calculate total utility (TU):

• $X=2$, $Y=16$: $TU=2(40)+16(10)=80+160=240$ (assuming MU for higher Y is constant).
• $X=4$, $Y=12$: $TU=4(20)+12(15)=80+180=260$.
• $X=6$, $Y=8$: $TU=6(10)+8(20)=60+160=220$.

The maximum utility is achieved at $X=4$ and $Y=12$, with $TU=260$.

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In the Real World

1. eSewa and Khalti: Budget Constraints in Digital Payments

• Idea Used: Budget constraint and consumer choice.
• How: When users allocate their monthly budget between eSewa/Khalti for bills, shopping, or transfers, they face trade-offs. For example, a user with Rs. 5,000 might choose between paying their Rs. 2,000 electricity bill (fixed expense) and spending the remaining Rs. 3,000 on groceries or savings. The marginal utility of spending on groceries (immediate satisfaction) vs. savings (future utility) drives their decision.
• Real Example: A student earning Rs. 20,000/month might allocate Rs. 5,000 for food, Rs. 3,000 for transport (using Pathao), Rs. 2,000 for tuition, and Rs. 10,000 for savings. The choice reflects their prioritization of utilities (e.g., education vs. entertainment).

2. Daraz and NEPSE: Marginal Utility in Purchases

• Idea Used: Law of diminishing marginal utility.
• How: When shopping on Daraz, the first item (e.g., a phone charger) gives high satisfaction (high MU), but the 10th item (e.g., a duplicate keychain) adds little extra satisfaction (low MU). Similarly, investors in NEPSE stocks experience diminishing returns as they buy more shares of the same company. The first share might feel exciting (high MU), but additional shares add less thrill (low MU).
• Real Example: Suppose a consumer buys 5 pairs of shoes from Daraz:
  • 1st pair: MU = 100 utils (excited to own new shoes).
  • 2nd pair: MU = 80 utils (still happy, but less thrilled).
  • 5th pair: MU = 20 utils (barely noticeable satisfaction). The consumer stops buying when MU approaches zero.

3. NTC and Ncell: Consumer Choice in Telecommunications

• Idea Used: Equi-marginal principle.
• How: Consumers choose between NTC and Ncell plans by comparing the "utility per rupee" of each. For example:
  • NTC offers 1GB data for Rs. 100 (MU = high for heavy internet users).
  • Ncell offers unlimited calls for Rs. 150 (MU = high for call-heavy users). A student might allocate their Rs. 500/month budget to maximize total utility by balancing data and call plans. If $\frac{M{U}_{\text{data}}}{P_{\text{data}}}=\frac{M{U}_{\text{calls}}}{P_{\text{calls}}}$, they achieve equilibrium.

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Applications of Utility Analysis

Advantages:

1. Predicts Consumer Behavior: Helps businesses forecast demand (e.g., Daraz adjusting inventory based on utility trends).
2. Pricing Strategies: Companies like Google Ads use marginal utility to set prices for targeted ads (e.g., higher bids for ads with higher perceived MU).
3. Policy Making: Governments use utility analysis to design subsidies (e.g., subsidizing rice to maximize poor households' satisfaction).
4. Resource Allocation: Banks allocate loans based on perceived utility (e.g., higher interest for riskier loans with lower MU).

Disadvantages:

1. Subjectivity: Utility is hard to measure numerically (cardinal utility criticism).
2. Assumes Rationality: Consumers may not always act rationally (e.g., impulse buys on Daraz).
3. Static Model: Ignores dynamic factors like changing tastes or income.
4. Limited to Two Goods: Real-world choices involve multiple goods and services.

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Exam Tip

1. Understand the Definitions: Know the difference between total utility (TU), marginal utility (MU), and average utility (AU). Be ready to calculate MU from TU data.

   • Example: If TU for 3 units is 100 and for 4 units is 110, then $M{U}_4=10$.

2. Budget Line Questions: Always plot the budget line correctly. Remember:

   • Intercepts are $\frac{M}{P_x}$ and $\frac{M}{P_y}$.
   • Slope is $-\frac{P_x}{P_y}$.
   • Shifts occur with changes in income ($M$) or prices ($P_x$ or $P_y$).

3. Consumer Equilibrium: The key formula is $\frac{M{U}_x}{P_x}=\frac{M{U}_y}{P_y}$. Always verify that the budget is fully spent in your answer.

4. Real-World Examples: Examiners love applications. Relate utility to:

   • Nepal: eSewa transactions, Daraz purchases, or NEPSE investments.
   • Global: Netflix subscriptions (diminishing MU of binge-watching), Uber rides (budget constraints), or Starbucks coffee choices.

5. Graphical Analysis: Practice drawing:

   • Marginal utility curves (downward-sloping).
   • Budget lines (straight lines with intercepts).
   • Consumer equilibrium points (tangency of indifference curves to budget lines—though this is covered in Unit 5, start visualizing it now).

6. Common Mistakes to Avoid:

   • Ignoring the budget constraint in equilibrium calculations.
   • Misinterpreting MU as always positive (it can be negative if consumption decreases).
   • Forgetting that utility maximization occurs where MU = 0 (last unit consumed).

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