Question

Your friend Sam has been asked to prepare appetizers for the university reception. She has an unlimited amount of ingredients and 6 hours in which to prepare them. Sam can make 300 minisandwiches or 150 servings of melon slices topped with smoked salmon and a dab of sauce per hour. \(\left[\mathrm{LO}_{2.1}\right]\) a. What is Sam's opportunity cost of making one mini-sandwich? b. What is Sam's opportunity cost of baking one melon appetizer? c. Suppose the reception has been postponed, and Sam has an extra 4 hours to prepare. What is the opportunity cost of making one mini-sandwich now? d. Suppose the reception has been postponed, and Sam has an extra 4 hours to prepare. What is the opportunity cost of making one melon appetizer now? e. Suppose Sam's friend Chris helps by preparing the melon slices, increasing Sam's productivity to 300 mini-sandwiches or 300 melon appetizers per hour. What is the opportunity cost of making one minisandwich now? f. Suppose Sam's friend Chris helps by preparing the melon slices, increasing Sam's productivity to 300 mini-sandwiches or 300 melon appetizers per hour. What is the opportunity cost of making one melon appetizer now?

Short answer

a. 0.5 melon appetizers b. 2 mini-sandwiches c. 0.5 melon appetizers d. 2 mini-sandwiches e. 1 melon appetizer f. 1 mini-sandwich

Step-by-step solution

Determine Opportunity Cost of Making One Mini-Sandwich

To find Sam's opportunity cost of making one mini-sandwich, we start by observing that Sam can make 300 mini-sandwiches or 150 melon appetizers per hour. The opportunity cost of producing one good is the amount of the other good that must be given up. For one mini-sandwich: Opportunity cost of 1 mini-sandwich = Number of melon appetizers forgone/Number of mini-sandwiches produced = 150/300 = 0.5. Therefore, the opportunity cost is 0.5 melon appetizers per mini-sandwich.

Determine Opportunity Cost of Making One Melon Appetizer

Similarly, the opportunity cost of making one melon appetizer is the number of mini-sandwiches Sam forgoes per melon appetizer. Opportunity cost of 1 melon appetizer = Number of mini-sandwiches forgone/Number of melon appetizers produced = 300/150 = 2. Thus, the opportunity cost is 2 mini-sandwiches per melon appetizer.

Opportunity Cost with Extended Time for Mini-Sandwich

If the reception is postponed and Sam has an additional 4 hours, her total time is now 10 hours. However, opportunity cost per unit does not change with more time since the rate of production per hour remains the same. So, the opportunity cost of 1 mini-sandwich remains 0.5 melon appetizers.

Opportunity Cost with Extended Time for Melon Appetizer

Similarly, with more time, the opportunity cost per melon appetizer will not change since the relative rate of production still holds. Thus, the opportunity cost of 1 melon appetizer remains 2 mini-sandwiches.

Opportunity Cost with Chris's Help for Mini-Sandwich

With Chris's help, Sam can now make 300 melon appetizers per hour (equal to the rate of mini-sandwich production). Thus, her rate of production per hour is 1:1 for both goods. Opportunity cost of 1 mini-sandwich with Chris = Number of melon appetizers forgone/Number of mini-sandwiches produced = 300/300 = 1. Therefore, the opportunity cost is 1 melon appetizer per mini-sandwich.

Opportunity Cost with Chris's Help for Melon Appetizer

Similarly, with Chris's help, the production possibility now allows 300 melon appetizers equal to mini-sandwiches per hour. Opportunity cost of 1 melon appetizer with Chris = Number of mini-sandwiches forgone/Number of melon appetizers produced = 300/300 = 1. So, the opportunity cost is 1 mini-sandwich per melon appetizer.

Key concepts

Production Possibility

The concept of a production possibility frontier (PPF) is critical in understanding how resources are allocated in any scenario. In Sam's case, with the capacity to produce 300 mini-sandwiches or 150 melon appetizers per hour, Sam faces a trade-off. This trade-off is graphically represented as a PPF, which illustrates the maximum potential output combinations of the two goods when resources are efficiently utilized.
If Sam decides to make only mini-sandwiches, she can produce a total of 1800 in her initial 6-hour window, while choosing to make only melon appetizers would result in 900 servings. This linear PPF shows how making more of one item limits the production of the other, ensuring that resources are fully and efficiently utilized.

• This line represents all possible production combinations.
• The slope of the line indicates the rate at which one good can be substituted for the other.
• It reveals the potential opportunity costs associated with switching between production options.

Rate of Production

In production scenarios, understanding the rate of production is essential for decision-making regarding which goods to produce. In Sam's kitchen, the rate of production is initially different for mini-sandwiches and melon appetizers:

• 300 mini-sandwiches per hour
• 150 melon appetizers per hour

These rates highlight Sam’s ability to produce certain items at specified speeds. They are vital for calculating opportunity costs and deciding which good to focus on, especially when the available time is limited.
When Chris joins Sam, this rate of production changes, allowing Sam to produce 300 of either the mini-sandwiches or melon appetizers per hour. Consequently, this equal rate shifts the relative advantage Sam may have had towards producing one good over another. As rates become equal, the opportunity costs become equivalent, impacting resource allocation decisions.

Resource Allocation

Resource allocation involves deciding how to distribute available resources like time and labor to maximize output. For Sam and Chris, their resource is time, and how they allocate this time determines what can be produced. Initially, without assistance, Sam has to choose how to best use her 6 hours of preparation time.

• If more mini-sandwiches are produced, fewer melon appetizers will be made.
• The goal is to find the optimal mix of both goods that satisfies needs and preferences for the reception.

With an additional 4 hours, Sam achieves more flexibility, yet the fundamental decision of "how much of each will be produced" remains similar in terms of opportunity cost. Thus, when Chris adds his labor, both production levels can rise independently, altering the decision dynamics.
Decisions are impacted by understanding opportunity costs, production possibilities, and maximizing output based on existing constraints.

Comparative Advantage

Comparative advantage explains how and why an individual or entity may choose to produce one type of good over another based on relative efficiency. Initially, Sam has a comparative advantage in producing mini-sandwiches, as their opportunity cost is lower than that of melon appetizers.

• Before Chris's help, making 1 mini-sandwich sacrifices only 0.5 melon appetizers.
• Conversely, each melon appetizer costs 2 mini-sandwiches.

However, Chris’s entry equalizes the production rate, which shifts the scenario. Now, each mini-sandwich equates to one melon appetizer. This change effectively removes Sam's prior comparative advantage in mini-sandwich production, as both goods are now produced at the same cost.
Sam's resource decision now pivots not on cost but on other factors such as demand at the reception or personal preference. Because of this change, understanding comparative advantage is vital, as it guides whether pursuing one type of good over another makes sound economic sense.