Darius buys only milk and cookies. a. In year 1 dollar Darius earns 100 dollar milk costs 2 dollar per quart, and cookies cost 4 dollar per dozen. Draw Darius's budget constraint. b. Now suppose that all prices increase by 10 percent in year 2 and that Darius's salary increases by 10 percent as well. Draw Darius's new budget constraint. How would Darius's optimal combination of milk and cookies in year 2 compare to his optimal combination in year \(1 ?\)

Microeconomics is the study of how individuals and firms make decisions and allocate resources. It delves into the behavior of economic agents like consumers, businesses, and governments, and how they interact in various market structures. Microeconomic analysis can include anything from why an individual chooses to buy more milk instead of cookies, to how a price change affects demand, or how taxes might impact consumer choices.

At the heart of microeconomics is the exploration of supply and demand, market equilibrium, and price mechanisms. It seeks to explain what drives people to make the economic choices they do, and how those choices affect resource distribution and the overall economy. For example, if the price of milk rises, microeconomics helps to predict whether Darius will continue buying the same amount of milk, switch to purchasing more cookies, or adjust his consumption in another way.

Consumer choice theory is a framework used in microeconomics to understand how consumers decide among the different products and services they could purchase. This theory assumes that consumers are rational and aim to maximize their utility, or satisfaction, given their budget constraints and the prices of goods and services.

In Darius's case, consumer choice theory would look at how he allocates his $100 budget to buy milk and cookies so as to get the most satisfaction. The theory suggests that Darius will consider his own preferences and the utility he derives from each additional quart of milk or dozen of cookies when deciding on his optimal consumption bundle. This is where the budget constraint becomes crucial; it represents all the combinations of milk and cookies Darius can afford, with the point at which Darius maximizes utility lying on this line.

Income and price changes have a direct impact on a consumer's budget constraint and subsequently on their optimal choice of goods. When income increases, the consumer can potentially purchase more goods, shifting the budget constraint outward, indicating more purchasing power. Conversely, if prices increase, the consumer's purchasing power diminishes.

In the exercise scenario, both Darius's income and the prices of milk and cookies rise by 10%. This simultaneous change maintains the slope of the budget constraint, but it does shift his budget line outward. Although Darius can still afford the same physical quantities as before, his actual purchasing decisions might change based on whether his preferences are more inclined towards either good or if they remain unchanged.

Understanding the Substitution and Income Effects

The impact of price changes on consumption can be broken down into two distinct parts: the substitution effect and the income effect. The substitution effect occurs when consumers react to a price change by purchasing more of the less expensive good. The income effect reflects how changes in purchasing power, due to a price change, alter consumption patterns. For Darius, since both his income and the prices increased proportionally, the substitution and income effects might cancel each other out, leaving his choice between milk and cookies potentially unchanged from year 1 to year 2.