Question

Suppose you're bowling with friends. You've already played one game and are trying to decide whether to play another. Each game costs \(\$ 6\) per person, plus a one-time rental fee of \(\$ 5\) for the bowling shoes. It would take another hour to play the next game, which would make you late to work. Missing an hour of work would mean that you would lose pay at a rate of \(\$ 12\) per hour. Based on this information, how much would you have to enjoy the next bowling game, expressed in terms of dollars, to play another game?

Short answer

You'd have to enjoy the next game at least \$18 to justify playing.

Step-by-step solution

Calculate the Total Cost of Bowling Another Game

First, determine the total monetary cost involved in bowling an additional game. Since you've already rented bowling shoes in the previous game and the problem specifies the shoes rental is a one-time fee, you don't pay this again. Therefore, the only additional cost for another game is the game cost itself.The cost per additional game is:\[ \text{Cost for another game} = \$6 \text{ (game cost) } \]

Account for Lost Wages

Next, calculate the opportunity cost in terms of lost wages. Playing another game makes you late to work, costing you potential earnings.Given that missing an hour of work results in losing \\(12, the opportunity cost is:\[ \text{Lost wages} = \\)12 \text{ per hour} \]

Total the Costs of Bowling One More Game

Add the cost of the game to the opportunity cost of the lost wages to find the total cost you incur by choosing to bowl another game instead of going to work:\[ \text{Total Cost} = \\(6 \text{ (cost of game)} + \\)12 \text{ (lost wages)} \]Calculating the total gives:\[ \text{Total Cost} = \$18 \]

Determine the Enjoyment Value Needed to Justify Bowling

You'd need to enjoy bowling enough to offset the total cost of \\(18. In economic terms, this means that the enjoyment value you derive from playing another bowling game must be equal to or greater than \\)18 for it to be a worthwhile decision.Thus, you have to value the enjoyment by at least \$18 to justify playing another game.

Key concepts

Understanding Marginal Cost

The concept of marginal cost is an essential aspect of decision making in economics. Marginal cost is the added cost incurred by producing or consuming one more unit of a good or service. In the bowling example, the marginal cost refers to the extra cost of playing an additional game. Since the shoe rental fee is a one-time charge, it doesn't increase with extra games. Therefore, the marginal cost of a second game is simply the cost of the game itself, which is \(\$ 6\).

Recognizing marginal cost helps in evaluating whether the benefits of an additional unit (here, another game) outweigh its extra costs. This aids in better decision making, especially when resources are limited.

• The marginal cost includes only the costs that change with the decision. Fixed costs, like the shoe rental fee, are not part of it after the initial purchase.
• Marginal cost is crucial when deciding how many units of a service to consume or produce, based on your budget or constraints.

Conducting a Cost-Benefit Analysis

Cost-benefit analysis is a systematic approach to weighing the strengths and weaknesses of alternatives. It involves comparing the total expected costs versus the benefits of an action. This analysis helps in making informed decisions.

In the context of bowling another game, you should compare the total cost, \(\\( 18\), against the enjoyment or value you expect to gain from that extra game. To make this decision, you need to assess:

• The direct costs, such as the cost of the additional game \(\\) 6\).
• The opportunity costs, like the lost wages of \(\$ 12\) from missing work.

Conducting a cost-benefit analysis ensures that all potential costs and benefits are weighed up, facilitating a rational decision-making process. By evaluating personal enjoyment value against total costs, you determine if proceeding with the additional game is justified.

Effective Decision Making

Decision making is a cognitive process that involves selecting a course of action among several alternatives. In economics, it's vital to consider all costs, both monetary and non-monetary, before deciding. The decision to play another game of bowling requires weighing the cost, \(\$ 18\), against how much you value that game.

This involves an evaluation of:

• Marginal costs, or the immediate additional expenses you will face.
• Opportunity costs, reflecting what you forego by choosing one option over another (e.g., lost wages).

Effective decision making means ensuring that the perceived benefits or enjoyment of an action outweigh its costs. It requires a balance between immediate satisfaction and longer-term consequences. Simple tools like cost-benefit analysis help guide these decisions, ensuring optimal utilization of resources.