In the last session, we talked about the different properties of isoquants. The ways that we, pro, the way, we depict graphically, how different combinations of input can be combined, produced different output levels. Now, one of the properties is that, they're convex, that the slope diminishes as we move toward greater use of the input on the horizontal axis. What economists call the slope of isoquants is the marginal rate of technical substitution. The rate at which we can trade off labor for capital and keep output the same. And, again from a slope perspective, rise over run, it's the, rate at which capital drops, as we move along an isoquant and add more labor And keep output the same. Now, intuitively, if we're at a particular point where we have to give up two units of capital in exchange for one unit of labor. So if the slope is negative 2 and if we put in an absolute value terms of the slope as 2. What that means is that each unit of labor is twice as productive as each unit of capital. If we have to trade off 2K for each L, then each L must be twice as productive as each unit of capital. So the slope also gives us the ratio of marginal productivities. But in inverse form because we're trading off capital for labor, so the relative productivities, and that must reflect inversely how powerful each unit of labor is productivity-wise versus each unit of capital. And let's go back to that former figure 7.3. Why might this slope decline? say we're producing revenue passenger miles in the airline business. It becomes more difficult to give up capital for labor, as we keep adding more labor and taking away capital. And end up with the same total number of passenger miles flown Or the other way, if we give up if we have less and less labor. the ability for us to give up further labor, and add capital we have to compensate with more and more capital. When we're down to just one pilot it'd have to be and extremely elaborate system that would allow us to fly those planes by remote control with the same safety level that we currently do with one pilot. So, it's not always the case, but most typically the case that these slopes are convex of isoquants. The rate at which we can trade off one input for the other, diminishes the more of a particular input we acquire. Now let's look at a particular example production of miles driven per year. Using two inputs of time and gasoline. There's a well-known relationship that we typically observe, that the faster you drive, the lower the miles per gallon. the engine, and the internal combustion engine of most cars, burns up more gasoline along the way. Say we want to achieve the isoquant of 6,000 miles per year. One way we could do it is by driving 60 miles per hour, and another way 55 miles per hour. To achieve 6,000 miles, and we drove 60 miles per hour, if we measure time on the horizontal axis, that first point, point A, it would take us 100 hours of driving to get to that output level of 6,000 miles. It would also take us 240 gallons of gasoline per year. Assuming that we get 25 miles per gallon driving 60 miles per hour. Let's also assume that if we drive more slowly, on average. [COUGH] 55 miles per hour. We get 26 miles per gallon. We get better mileage per, per gallon. Slower speed, means that it'll take us 109 hours, if you do the math, to drive that same 6,000 miles but now driving at 55 miles per hour, but we'll save some gas along the way. Instead of consuming 240 gallons per year we'll only consume 231. Driving slower again we assume 26 miles per gallon. Should we be at point a or point b? It turns out this isoquant just gives us the relative productivities between these two different inputs and the trade off involved between those relative productivities. We also to make the decision, we'll have to figure out the costs of those different inputs. If you use fewer gallons, nine fewer gallons say that the average cost per gallon is $4, you'll end up saving $36 a year. Is it worth it? Well, the key thing will depend on how much your time is worth. You'll also add $9 nine hours a year on the freeways, or on the roads driving. And it'll depend on each of those hours, are they worth more than $4 per hour to you? Of course there are other factors involved, if you drive more slowly in general, it tends to be safer, and we'd have to factor that into the analysis. So we've dramatically simplified, but showed how these trade offs between different inputs into producing 6,000 miles, and the relative productivities. And then point it to how the costs of these two inputs will also help ultimately make, lead us to the right production decision.