Question

Your friend Sam has been asked to prepare appetizers for a university reception during homecoming weekend. She has an unlimited amount of ingredients but only 6 hours to prepare them. Sam can make 300 mini-sandwiches or 150 servings of melon slices topped with smoked salmon and a dab of sauce per hour. [LO 2.1] a. Draw Sam's production possibilities frontier. b. Now suppose that the university decides to postpone the reception until after the big game, and Sam has an extra 4 hours to prepare. Redraw her production possibilities frontier to show the impact of this increase in resources. c. Now, in addition to the extra time to prepare, suppose Sam's friend Chris helps by preparing the melon slices. Sam can now make 300 mini-sandwiches or 300 melon appetizers per hour. Redraw Sam's production possibilities frontier to show the impact of increased productivity in making melon appetizers.

Short answer

The PPF shifts outward with more time and increases further with help.

Step-by-step solution

Understand the Basics

First, we need to determine Sam's production capabilities within the initial 6-hour time frame. She can produce 300 mini-sandwiches or 150 melon appetizers per hour. In 6 hours, this means she can make either 1800 mini-sandwiches or 900 melon appetizers.

Draw Initial Production Possibilities Frontier (PPF)

The PPF is a graph that shows the combinations of two goods that can be produced with given resources. For Sam, if she uses all 6 hours to make mini-sandwiches, she can make 1800 mini-sandwiches and 0 melon appetizers (point A). If she spends all 6 hours on melon appetizers, she can produce 0 mini-sandwiches and 900 melon appetizers (point B). The PPF is a straight line connecting points A and B, showing all possible combinations.

Extend the Time for More Production

With 4 extra hours, Sam now has a total of 10 hours. At the same rate, she can produce 3000 mini-sandwiches (300 * 10) or 1500 melon appetizers (150 * 10). Her new PPF would be extended to reflect 3000 mini-sandwiches and 0 melon appetizers at one extreme and 0 mini-sandwiches and 1500 melon appetizers at the other.

Redraw PPF with Additional Help

With Chris's assistance, Sam's production rate for melon appetizers doubles to 300 per hour. Now, in 10 hours, she can make 3000 melon appetizers instead of the previous 1500. The new PPF would connect 3000 mini-sandwiches and 0 melon appetizers to 0 mini-sandwiches and 3000 melon appetizers, reflecting her augmented capacity with Chris's help.

Key concepts

Opportunity Cost

Opportunity cost is a fundamental concept in economics and relates closely to decision-making. It refers to the value of the best alternative that is forfeited when a decision is made. For Sam, choosing to spend one hour making mini-sandwiches means she cannot use that time to make melon appetizers. Therefore, the opportunity cost of making one mini-sandwich is the number of melon appetizer servings she could have produced instead (and vice versa). By knowing the opportunity cost, Sam can make informed choices about how to best use her time.
Understanding opportunity cost allows for more strategic planning in resource utilization. In Sam's case, recognizing that each sandwich made costs her the opportunity to produce melon appetizers helps her determine the most efficient allocation of her time given her needs and preferences.

• It helps in comparing the benefits derived from different choices.
• Keeps resources moving fluidly by tracking trade-offs.
• Enables better prioritization in production and consumption.

Resource Allocation

Resource allocation involves deciding how to distribute limited resources among competing uses to make the most of them. Sam has 6 hours initially, which must be divided between two activities: making mini-sandwiches or melon appetizers. With limited time, she needs to decide which combination optimally meets her objective for the event.
When the university postponed the reception, providing more preparation time, Sam’s total available time increased to 10 hours. This change allowed her more freedom in resource allocation, giving her the capacity to make both more sandwiches and more melon servings. She can allocate the additional hours in a manner that aligns with her production goals and desired output for the reception.
Resource allocation is about finding the best possible distribution to achieve a desirable outcome. Sam’s friend Chris also plays into this, as they enhance the production capacity for melon appetizers, altering the allocation dynamics.

• Involves optimal decision-making to get the most benefit.
• Accounts for all available resources such as time, skills, and labor.
• Impactful in unexpected scenarios, like the event postponement.

Marginal Rate of Transformation

The Marginal Rate of Transformation (MRT) represents the trade-off between two goods when reallocating resources from one to another on the production possibilities frontier (PPF). It indicates how many units of one good must be reduced to produce an additional unit of another good.
For Sam, MRT is the slope of the PPF and shows the rate at which mini-sandwiches must be given up to produce more melon appetizers. In the initial scenario, the MRT is determined by her original ability to make either 300 mini-sandwiches or 150 melon appetizers per hour. This boils down to an MRT of 2:1, meaning Sam needs to give up two mini-sandwiches to gain one melon appetizer.
As more resources become available (extra time or help from Chris), the MRT will change. With Chris doubling the rate for melon appetizers, the MRT becomes equal, allowing Sam to adjust her production more fluidly.

• MRT captures the opportunity cost in practical terms on the PPF.
• Adapts based on efficiencies or changes in resources.
• Guides economical production decisions.

Efficiency

Efficiency in the context of a production possibilities frontier means utilizing resources in such a way that production is maximized without any waste. For Sam, being efficient means she uses all her available time to produce the maximum possible combination of mini-sandwiches and melon appetizers.
The original graph of Sam's efficiency was demonstrated by a straight line on the PPF, indicating all potential combinations she can achieve personally in six hours. With the added time, Sam's resource pool increases, expanding her efficient frontier. When Chris steps in to help, further improvement in efficiency is noticed with the possibility to produce even more with the same amount of time.
Achieving efficiency ensures no resources are left unused, and every action taken reaches the highest possible output. Sam can achieve this by staying along the PPF line, ensuring that every decision maximally utilizes her time for preparing the food that best fits the reception's needs.

• Keeps production balanced and at maximum capacity.
• Involves adjusting strategy based on changes in available resources.
• Reflects purposeful and informed management of resources.