3.1 Resource Constraints

Even before Chuck is marooned on his island, he’s keenly aware of the concept of resource constraints. In the opening scene of “Cast Away,” he exhorts his crew to meet a harsh deadline for getting packages delivered to the Moscow airport:

"Time rules over us without mercy...That's why every FedEx office has a clock. Because we live or we die by the clock...Locally, it's 1:56. That means we've got three hours and four minutes before the end-of-the-day's package sort. That's how long we have — that's how much time we have — before this pulsating, accursed, relentless taskmaster tries to put us out of business."

You could be the richest person in the world, but time would still constrain your activities: even if you could afford whatever you wanted, you would only have a finite amount of time with which to enjoy it. Time is the ultimate resource constraint: an hour spent doing one thing is one hour less spent doing something else. Much of economic activity boils down to how we spend our time.

In the last chapter, we saw how time — in the form of labor input, and in conjunction with other inputs — may be transformed into a single good via a production function. In this chapter, we will examine the issue of allocating a fixed set of resources across goods, and what effect resource constraints have on what combinations of goods we can produce. After all, an hour spent producing one good is an hour less producing another.

In Chuck’s case, once he is stranded on his island, how he spends his time becomes even more important. Let’s assume Chuck can spend his time in only two ways: fishing or cracking coconuts open. Let’s call fish “good 1” and coconuts “good 2,” so we’ll call the labor devoted to fish $L_1$ and the labor devoted to coconuts $L_2$. Finally, let’s call the total amount of time Chuck has available to him (say, hours per week) $\overline L$. In this case Chuck’s resource constraint is given by the equation \(L_1 + L_2 \le \overline L\) We can visualize his tradeoff of how to spend his time by plotting “labor devoted to fish” and “labor devoted to coconuts” on a graph:

Next, let’s see how Chuck’s choice of how to allocate his resources affects the combinations of goods he can produce.