Question

The price of DVDs \((D)\) is \(\$ 20\) and the price of \(\operatorname{CDs}(C)\) is \(\$ 10 .\) Philip has a budget of \(\$ 100\) to spend on the two goods. Suppose that he has already bought one DVD and one CD. In addition, there are 3 more DVDs and 5 more CDs that he would really like to buy. a. Given the above prices and income, draw his budget line on a graph with CDs on the horizontal axis. b. Considering what he has already purchased and what he still wants to purchase, identify the three different bundles of CDs and DVDs that he could choose. For this part of the question, assume that he cannot purchase fractional units.

Short answer

Philip's budget line will run from the point (10,0) to the point (0,5) considering his original budget of $100. Given his remaining budget of $70 after his initial purchases and the cost of the additional items he desires, he can choose from these combinations: (i) 2 more DVDs and 1 more CD, (ii) 1 more DVD and 3 more CDs, or (iii) no more DVDs and 7 more CDs.

Step-by-step solution

Calculation of the maximum units of DVDs and CDs Philip can buy

Before drawing the budget line, it is essential to find out how many CDs and DVDs Philip can buy with his budget. The price of a DVD (D) is $20 and the price of a CD (C) is $10. Given his budget of $100, without considering his initial purchases and his wish list, the maximum possible CDs he can buy: \( \frac{budget}{\text{price of CD}} = \frac{100}{10} = 10 \) Whereas the maximum DVDs he can purchase is \( \frac{budget}{\text{price of DVD}} = \frac{100}{20} = 5 \)

Draw the budget line

The budget line will be a straight line from the point (10,0) to the point (0,5) on a graph where CDs are on the horizontal axis and DVDs on the vertical axis. This line represents all combinations of CDs and DVDs Philip can buy with his initial budget.

Identify possible bundles

Taking into account Philip's initial purchases (1 DVD and 1 CD) and considering that he still wants more (3 DVDs and 5 CDs), it's required to calculate possible combinations he could buy with his remaining budget. Initially, after purchasing 1 DVD and 1 CD, he has \(100 - 20 - 10 = \$70\) left. If he buys the additional 3 DVDs and 5 CDs he wants, this would cost him another \(3*20 + 5*10 = \$110\), which is more than his remaining budget. Therefore, he has to make choices. He could decide to buy 2 more DVDs and 1 more CD with his remaining budget (costing \(2*20 + 1*10 = \$50\)), or he could choose to buy 1 extra DVD and 3 extra CDs (costing \(1*20 + 3*10 = \$50\)), or finally he could decide to buy no extra DVDs and 7 extra CDs (costing \(7*10 = \$70\)). All these combinations are feasible given his remaining budget.

Key concepts

Budget Constraint

Understanding the concept of a budget constraint is pivotal in grasping the fundamentals of microeconomics. Simply put, a budget constraint represents all the combinations of goods and services a consumer can purchase given their income level and the prices of those goods. In the context of our exercise, Philip has a budget of \(100 to allocate between DVDs and CDs, priced at \)20 and $10 respectively.

Let's visualize Philip's budget constraint graphically: If we place CDs on the horizontal axis and DVDs on the vertical axis, we can draw a straight line between the maximum number of each item he could afford if he only purchased one of them. The intercepts on the axes are found by dividing Philip's budget by the price of each good — the end points being (10, 0) for CDs and (0, 5) for DVDs. The slope of this line will be negative because to buy more of one good, Philip must give up some of the other, reflecting the principle of trade-offs. This constraint line essentially defines Philip's consumption possibilities, and any combination of CDs and DVDs that lies on this line will exhaust his budget completely.

Consumer Choice Theory

Consumer choice theory delves into how we make decisions given our preferences and budget constraints. Each individual consumer aims to get the most satisfaction, or 'utility', out of their purchases. However, they must make choices based on their financial limitations, which is precisely what Philip is experiencing.

Philip's preferences are clear: he desires more of both DVDs and CDs, but his budget limits him to choosing between multiple bundles. Consumer choice theory utilizes the budget constraint to illustrate the concept of 'utility-maximizing combinations' — points on or beneath the budget line where the consumer gets the highest satisfaction. When faced with the dilemma of selecting between 3 DVDs and 5 CDs, Philip's optimal choice will depend on his personal preferences. The question prompts exploration into these preferences without going into numerical utility values, but it implies considering which bundle of goods will bring Philip the most satisfaction without exceeding his constrained budget.

Opportunity Cost

The concept of opportunity cost is one of the most crucial in economics, which refers to the value of the next-best alternative when a decision is made; it's what is foregone when we choose one option over another. In our exercise, this means that every time Philip chooses to purchase a DVD or a CD, he incurs an opportunity cost by forgoing the other item. For example, if he buys one DVD, the opportunity cost is the two CDs he could have bought with the same money.

The idea of opportunity cost becomes even more tangible when Philip must decide between additional bundles of CDs and DVDs he wants. By choosing to purchase an additional 2 DVDs, he foregoes the possibility to buy 4 CDs with the same funds. The concept reminds us that every choice has a trade-off, and while the budget line shows us all the tangible possibilities within reach, opportunity cost tells us about the invisible cost associated with each choice. When Philip evaluates his options, he's not only considering his budget constraint but also the opportunity cost of each potential bundle of goods.