Question

An economy has 5 workers. Each worker can make 4 cakes or 3 shirts. (a) Draw the production possibility frontier. (b) How many cakes can society get if it does without shirts? (c) What points in your diagram are inefficient? (d) Can the economy produce an output combination which lies above the production possibility frontier? (e) What is the opportunity cost of making a shirt and making a cake? (f) Does the law of diminishing returns hold in this economy?

Short answer

(a) PPF endpoints: (0, 20) cakes and (15, 0) shirts. (b) 20 cakes without shirts. (c) Points inside the PPF are inefficient. (d) Cannot produce above the PPF. (e) Opportunity cost: 1 shirt = 4/3 cakes; 1 cake = 3/4 shirts. (f) No diminishing returns in this scenario.

Step-by-step solution

Understanding the Scenario

The problem involves an economy with 5 workers. Each worker can produce either 4 cakes or 3 shirts. We need to analyze different output combinations based on these capacities.

Drawing the Production Possibility Frontier (PPF)

The PPF is a graphical representation showing the maximum quantities of two products that an economy can produce with a given set of resources. If all 5 workers make cakes, they can produce \(5 \times 4 = 20\) cakes. If all make shirts, they can produce \(5 \times 3 = 15\) shirts. The PPF will be a straight line with endpoints at (0, 20) on the cake axis and (15, 0) on the shirt axis.

Calculating Maximum Cakes Without Shirts

If no shirts are produced, all 5 workers can concentrate on making cakes. Consequently, society can produce the maximum of 20 cakes.

Identifying Inefficient Points

Inefficient points lie inside the PPF, where not all resources are fully utilized. Any combination of cakes and shirts below the straight line connecting (0,20) and (15,0) is considered inefficient.

Discussing Feasibility Above PPF

Points above the PPF are unattainable given current resources and technology, meaning the economy cannot produce beyond the line where full resource utilization is assumed.

Determining Opportunity Cost

The opportunity cost is the forgone production of one good when resources are allocated to another. Making one shirt costs \(\frac{4}{3}\) cakes because each worker switches from producing 4 cakes to 3 shirts, converting 1 shirt into a sacrifice of 4/3 cakes. Conversely, making one cake costs \(\frac{3}{4}\) of a shirt.

Evaluating the Law of Diminishing Returns

The law of diminishing returns suggests that beyond a certain point, adding more of a factor of production results in smaller increases in output. In this simple model where resources are fully interchangeable between cakes and shirts, diminishing returns are not showcased since each worker can consistently trade between making fixed amounts of cakes or shirts.

Key concepts

Opportunity Cost

Opportunity cost is a crucial concept that helps understand the trade-offs in resource allocation. In this scenario, we calculate what is sacrificed when choosing to produce one good over another. For this economy with 5 workers, if resources are redirected to make 3 shirts instead of 4 cakes per worker, then making 1 shirt comes at the expense of losing approximately \(\frac{4}{3}\) cakes. Conversely, producing 1 cake would mean giving up \(\frac{3}{4}\) of a shirt.
The opportunity costs are derived by considering the units of each good foregone to produce an additional unit of the other good. This information aids producers in making informed decisions on how to allocate their resources effectively.
Understanding opportunity cost helps in recognizing the potential benefits lost, thereby guiding efficient decision-making in achieving economic goals.

Law of Diminishing Returns

The law of diminishing returns describes a point at which the addition of resources results in a decreasing rate of output increase. In our simplified economy model consisting of workers switching entirely between two products, the law doesn’t apply directly. Each worker's output capacity remains constant whether they're making cakes or shirts.
Since the workers can interchangeably produce cakes and shirts without diminishing output per worker, we don't observe diminishing returns in this scenario. This model assumes complete flexibility and equal productivity in the resources dedicated to each good. However, in more complex economies where additional inputs lead to less proportional increases in output, diminishing returns would be more evident.
Understanding this concept is essential for real-world businesses as it helps optimize the level of resource inputs to achieve the best possible efficiency.

Resource Allocation

Resource allocation refers to how an economy decides to utilize its limited resources to optimize output of different goods. In our example, the economy has to choose between distributing its 5 workers to produce either cakes or shirts.

• If all resources are focused on cakes, a maximum of 20 cakes is possible.
• If all resources are fully devoted to shirts, the maximum production is 15 shirts.

These choices and the proportions in which resources are allocated determine the production possibility frontier (PPF). The PPF illustrates the trade-offs and potential outputs that can be achieved by reallocating resources, allowing economies to visualize the most efficient use of resources given their current capacities.
Proper resource allocation ensures maximum output efficiency, contributing to an economy's overall productivity and growth.

Inefficient Production Points

Inefficient production points are combinations of products that fail to utilize all available resources fully. On a production possibility frontier (PPF) diagram, they appear below the line, indicating that the economy is operating within its capacity but not using it optimally.
In the case of the 5-worker economy, any point below the straight line connecting (0, 20) cakes and (15, 0) shirts is inefficient. It means some workers are not being used productively, leading to wasted potential.

• These inefficiencies might result from misallocation of labor or other resources, technological constraints, or other disruptions.
• Identifying such points helps in strategizing better resource management so the economy can work towards full capacity utilization on the PPF line.

It’s crucial for economies to identify and eliminate inefficiencies to boost productivity and maintain a competitive edge.