Question

Suppose that Canada produces two goods: lumber and fish. It has 18 million workers, each of whom can cut 10 feet of lumber or catch 20 fish each day. \(\left[\mathrm{LO}_{2} .1\right]\) a. What is the maximum amount of lumber Canada could produce in a day? b. What is the maximum amount of fish it could produce in a day? c. Write an equation describing the production possibilities frontier, in the form described on pp. \(28-29\) d. Use your equation to determine how many fish can be caught if 60 million feet of lumber are cut.

Short answer

a. 180 million ft; b. 360 million fish; c. \( L = 180 - 0.5F \); d. 240 million fish.

Step-by-step solution

Calculate Maximum Lumber Production

To find the maximum amount of lumber Canada could produce in a day, multiply the number of workers by the amount of lumber each worker can cut. With 18 million workers and each able to cut 10 feet of lumber, the calculation is:\[ \text{Maximum Lumber} = 18 \text{ million workers} \times 10 \text{ feet of lumber/worker} = 180 \text{ million feet of lumber} \]

Calculate Maximum Fish Production

To find the maximum number of fish Canada could catch in a day, multiply the number of workers by the amount of fish each worker can catch. With 18 million workers and each able to catch 20 fish, the calculation is:\[ \text{Maximum Fish} = 18 \text{ million workers} \times 20 \text{ fish/worker} = 360 \text{ million fish} \]

Establish Production Possibilities Frontier (PPF) Equation

The production possibilities frontier (PPF) shows the trade-off between two goods. Assume that all resources are used to either produce lumber or fish. Let \( L \) represent feet of lumber and \( F \) the number of fish. The PPF equation is derived from the total labor constraint:\[ \frac{L}{10} + \frac{F}{20} = 18 \text{ million} \]Simplifying gives the PPF equation:\[ L = 180 - 0.5F \] (Note: Units are in millions.)

Calculate Fish Production for Given Lumber Output

To find the number of fish that can be caught when 60 million feet of lumber are produced, substitute \( L = 60 \) into the PPF equation and solve for \( F \):\[ 60 = 180 - 0.5F \]\[ 0.5F = 180 - 60 \]\[ 0.5F = 120 \]\[ F = 240 \]So, 240 million fish can be caught if 60 million feet of lumber are cut.

Key concepts

Opportunity Cost

In economics, opportunity cost represents the benefits an individual, investor, or business misses out on when choosing one alternative over another. For Canada, this means considering the foregone production of one good to produce more of another: lumber or fish. If a Canada worker cuts 10 feet of lumber one day, they miss the chance to catch 20 fish in that same day.
In this case, the opportunity cost helps determine the relative value of different production decisions. For lumber, the opportunity cost per 10 feet cut is 20 fish because producing more lumber means catching fewer fish and vice versa. The concept works as a guide for the country to optimize its production decisions and allocate labor effectively.
Opportunity cost isn't just numbers. It's a crucial decision-making tool that applies across various resources like time, money, and labor. Understanding opportunity costs can lead to more efficient economic outcomes and aid in planning future resource allocation strategies.

Trade-offs in Economics

Trade-offs in economics involve balancing priorities and making decisions about resource allocation and production. Canada, with a finite number of 18 million workers, can either produce lumber or catch fish, but not both to their maximum extent simultaneously. The trade-off here is between the two goods given limited resources.
This trade-off is illustrated in the Production Possibilities Frontier (PPF), which visually shows combinations of amounts of lumber and fish Canada can produce. A point along the PPF reflects a balance where utilizing all resources for one product reduces supply for the other. Choosing one production level means decreasing the ability to produce more of the alternate good.
Understanding trade-offs is fundamental in economics because it guides decisions with resource shortages. It involves analyzing margins and optimizing outputs while keeping costs in check. With trade-offs, decision-makers can identify efficient allocations that achieve goals by prioritizing resources most effectively.

Resource Allocation

Resource allocation is the method of assigning available resources among various projects or uses. In the question, Canada must determine how to use its 18 million workers to maximize lumber or fish production. Each decision affects how resources contribute to different outputs.
The production possibilities frontier (PPF) equation, \( L = 180 - 0.5F \), encapsulates the complex decisions of resource allocation. It expresses possible distributions of labor among lumber production or fishing. From this, Canada can decide which goods to focus more on based on current or expected demand, prices, and other economic factors.
Efficient resource allocation means striking a balance where resources are not wasted. Proper allocation helps optimize productivity and profits, ensuring economic activities align with national priorities and market demand. Understanding resource allocation can not only benefit nations but individuals and businesses in successfully managing limited resources.