Consumer choice is all about making smart decisions with limited resources. It's like planning the ultimate pizza party on a budget. You've got to figure out how many pizzas and sodas you can afford, and which combo will make everyone happiest.

The budget constraint is your spending limit, like how much cash you've got for the party. Opportunity cost comes into play when you decide between extra toppings or more drinks. It's all about finding that sweet spot where you get the most bang for your buck.

Consumer Choice and Budget Constraints

Budget constraints and feasible consumption

• Budget constraint represents all possible combinations of two goods a consumer can afford given their income and the prices of the goods
  • Graphically represented by a straight line on a graph with the quantities of the two goods on the axes
  • Slope of the budget line is the negative ratio of the prices of the two goods, calculated as $-P_x/P_y$ (e.g., if the price of good X is $2 and the price of good Y is $4, the slope would be -1/2)
• Budget line equation summarizes the budget constraint algebraically: $P_x X + P_y Y = I$
  • $P_x$ and $P_y$ represent the prices of goods X and Y respectively (e.g., price of a hamburger and price of a pizza)
  • $X$ and $Y$ represent the quantities of goods X and Y the consumer chooses to purchase
  • $I$ represents the consumer's income available for spending on the two goods
• Feasible consumption choices are all combinations of goods that lie on or below the budget line
  • These choices are affordable for the consumer given their income and the prices of the goods (e.g., 2 hamburgers and 3 pizzas)
• Infeasible consumption choices are combinations of goods that lie above the budget line
  • These choices are not affordable for the consumer given their income and the prices of the goods (e.g., 6 hamburgers and 5 pizzas)

Opportunity costs in decision-making

• Opportunity cost is the next best alternative foregone when making a choice
  • Represents the trade-off between consuming one good versus another (e.g., choosing to buy a hamburger means forgoing the opportunity to buy a slice of pizza)
• Marginal rate of transformation (MRT) is the slope of the budget line and measures the opportunity cost of consuming one more unit of a good in terms of the other good
  • Formula for calculating MRT: $MRT = -P_x/P_y$ (e.g., if the price of a hamburger is $2 and the price of a pizza is $4, the MRT is -1/2, meaning the opportunity cost of one pizza is 2 hamburgers)
• Optimal consumption choice occurs at the point where the consumer's marginal rate of substitution (MRS), which represents their preferences, equals the marginal rate of transformation (MRT), which represents the market trade-off between the two goods
  • At this point, the consumer maximizes their satisfaction given their budget constraint
  • This point of tangency between the indifference curve and budget line is known as consumer equilibrium

Law of diminishing marginal utility

• Utility measures the satisfaction or happiness derived from consuming a good or service
• Marginal utility is the additional satisfaction gained from consuming one more unit of a good or service
• Law of diminishing marginal utility states that as a consumer consumes more of a good, the marginal utility derived from each additional unit decreases, assuming other factors remain constant (ceteris paribus)
  • For example, the first slice of pizza provides more satisfaction than the third slice consumed in one sitting
• Diminishing marginal utility leads to a downward-sloping demand curve because as the price of a good decreases, consumers are willing to buy more of the good since the additional utility gained from each unit is less than the utility gained from the previous unit

Marginal analysis for rational choices

• Marginal analysis involves evaluating the additional benefits and costs of an activity
  • Rational decision-making compares marginal benefits and marginal costs (e.g., comparing the additional satisfaction gained from consuming one more unit of a good to the additional cost of purchasing that unit)
• Optimal consumption choice occurs when the marginal utility per dollar spent on each good is equal
  • Formula: $MU_x/P_x = MU_y/P_y$ (e.g., if the marginal utility of a hamburger is 20 utils and its price is $2, and the marginal utility of a pizza is 40 utils and its price is $4, the optimal choice is to consume both goods since the marginal utility per dollar is equal at 10 utils per dollar)
  • If the marginal utility per dollar is not equal for all goods, the consumer can increase their total utility by reallocating their spending towards the good with the higher marginal utility per dollar
• Corner solution occurs when the optimal consumption choice involves consuming only one of the two goods because the marginal utility per dollar of that good is always higher than the other, given the consumer's budget constraint
• Interior solution occurs when the optimal consumption choice involves consuming a combination of both goods because the marginal utility per dollar is equal for both goods at the chosen consumption point

Consumer preferences and behavior

• Indifference curves represent combinations of goods that provide the same level of satisfaction to a consumer
• Changes in income or prices can lead to income and substitution effects, which explain how consumers adjust their consumption patterns
• Revealed preference theory suggests that consumers' actual choices reveal their underlying preferences