Consumer Choices on a Limited Income

Consider a consumer who can buy only two items with a set quantity of money (income). The market sets the prices for the goods. When a consumer is unable to purchase any and every possible combination of the two things she might desire to use, it is called consumer’s budget constraint. 

The consumer’s possible consumption bundles are determined by the cost of the commodities and their income. The consumer can only afford to purchase bundles that cost her less than or equal to her fixed income given the costs of the two commodities and her limited income.

Budget Set and Budget Line: Insight into Choices through Budget Sets and Lines

• Components of the Consumer’s Budget (Income and Prices): The consumer’s income is M, and the prices of bananas and mangoes are P1 and P2respectively. 
  • To buy a bundle of bananas(x1) and mangoes(x2), the consumer must spend P1 x1 +  P2 x2money.
• Consumer’s Budget Constraint: The consumer can choose any bundle as long as it costs less than or equal to their income.  
  • This inequality is called the consumer’s budget constraint.

Budget Set: It is the collection of all bundles available to the consumer at market prices.

• The consumer’s budget set includes all bundles (x1, x2) with numbers greater than or equal to 0 and P1x1 +  P2 x2 ≤ M, represented in a diagram like Figure ,
• All bundles in the positive quadrant which are on or below the line are included in the budget set. The equation of the line is P1x1 +  P2x2 = M. 

• The Budget Line: It represents bundles with cost equal to M, while points below it represent those with cost less than M.

x2 = (M/P2)-(P1/P2)x1

• Budget Line Characteristics: The budget line is a straight line with horizontal intercept M/p1 and vertical intercept M/p2. 
  • The Horizontal Intercept: It represents the bundle that the consumer can buy if she spends her entire income on bananas. 
  • The Vertical Intercept: It represents the bundle that the consumer can buy if she spends her entire income on mangoes.
  • The slope of the budget line is p1/p2.

• Example: For a consumer with Rs 20, the available bundles are (0, 0, 1, 0, 2), (0, 3), (0, 4), (1, 0), (2, 1), (3, 1), and (4, 0). However, bundles like (3, 3) and (4, 5) cost more than Rs 20 due to their higher prices.

Price Ratio and the Slope of the Budget Line: Striking a Balance

• A Consumer’s Budget Line: It represents a bundle of goods that cost the consumer their entire budget. 
• To buy one more banana, the consumer must reduce their expenditure on mangoes by p1 amount. 
• This means they must give up p1/p2 quantities of mangoes to have an extra quantity of bananas.

Changes in the Budget Set: Income and Price Impact

• Income Change and The Budget Set: The set of available bundles depends on the prices of goods and the consumer’s income.
  • If the consumer’s income changes from M to M′, they can afford to buy all bundles with prices p1 x1 + p2 x2 ≤ M′.
  • Now the equation of the budget line is p1 x1 + p2 x2 = M′ or  x2= (M’/p2)-(p1/p2)x1.
  • The new budget line slope remains the same as before income change, but the vertical intercept changes.
• Effects of Income on the Budget Set: Shifting Budget Lines for Consumer Choices
  • Increased income leads to an outward shift in the budget line, allowing consumers to buy more goods at market prices. 
  • Conversely, decreased income decreases both intercepts, causing an inward shift.
• Price Changes and the Budget Set: Now suppose the price of bananas change from p1 to p’1 but the price of mangoes and the consumer’s income remain unchanged.
  • At the new price of bananas, the consumer can afford to buy all bundles (x1, x2 ) such that p’1 x1 + p2 x2 ≤ M. 
  • The equation of the budget line is p’1 x1 + p2 x2 = M or  x2= (M’/p2)-(p’1/p2)x1 
  • The vertical intercept of the new budget line remains the same as before the change in banana prices. 
  • However, the slope and horizontal intercept change after the price change.
    • If banana prices increase, the budget line becomes steeper, while if they decrease, it becomes flatter. 
  • The budget set changes when only one commodity changes, and a change in mango prices results in similar changes.

Optimal Choice of the Consumer: Deciphering Optimal Choices and Preferences 

• Determinants of Optimal Consumer Choices: Normally, the amount of a good that the consumer chooses optimally, depends on –
  • The price of the good itself, the prices of other goods, the consumer’s income and her tastes and preferences.
• Importance of the Budget Set: The budget set contains all available bundles for consumers to choose their consumption bundle. 
• Consumer Preferences and Bundle Selection: Consumers choose their bundles based on their preferences and tastes, with well-defined preferences over all possible bundles. 
  • They can compare and either prefer or be indifferent to any two bundles.
• Consumer Preferences: In economics, a rational consumer has well-defined preferences over available bundles and acts according to them. 
  • A rational  consumer’s problem is to move to the highest possible indifference curve given their budget set. 
• The Optimum Point: It is located on the budget line, where the consumer’s preferences are monotonic. 
  • Points below the budget line are preferred, and points above the line are not available. 
• The Optimum Bundle: It is located at the point where the budget line is tangent to an indifference curve, as any point on the line other than the point where it touches the indifference curve lies on a lower indifference curve and cannot be the consumer’s optimum.
  • Figure  shows the consumer’s optimum, where the budget line is tangent to the black indifference curve. 

• The highest possible indifference curve is at the budget line, while points above, below, and below it are not affordable. 
  • Therefore, (x*1, x*2) is the consumer’s optimum bundle.

Equality of the Marginal Rate of Substitution and the Ratio of the Prices: Balance of Trade-offs

• The Optimum Consumer Bundle: It is at a point where the budget line is tangent to an indifference curve. 
• Same Slope: At this point, the slope of the indifference curve (MRS) and the budget line (price ratio) should be the same. 
• Preference Bundles and Market Substitution: However, if the MRS is greater than the price ratio, the consumer cannot substitute one good for another in the market, leading to a preference bundle. 

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