MRS is used in indifference theory to analyze consumer behavior. The marginal rate of substitution MRS formula is:. The marginal rate of substitution is a term used in economics that refers to the amount of one good that is substitutable for another and is used to analyze consumer behaviors for a variety of purposes.
MRS is calculated between two goods placed on an indifference curve , displaying a frontier of utility for each combination of "good X" and "good Y. The slope of the indifference curve is critical to the marginal rate of substitution analysis. Essentially, MRS is the slope of the indifference curve at any single point along the curve. Since most indifference curves are curves, the slopes will be different as one moves along them.
Most indifference curves are usually convex because, as you consume more of one good, you will consume less of the other. Indifference curves can be straight lines if a slope is constant, resulting in an indifference curve represented by a downward-sloping straight line.
If the marginal rate of substitution is increasing, the indifference curve will be concave to the origin. This is typically not common since it means a consumer would consume more of X for the increased consumption of Y and vice versa.
Usually, marginal substitution is diminishing, meaning a consumer chooses the substitute in place of another good, rather than simultaneously consuming more. The law of diminishing marginal rates of substitution states that MRS decreases as one moves down a standard convex-shaped curve, which is the indifference curve. For example, a consumer must choose between hamburgers and hot dogs. To determine the marginal rate of substitution, the consumer is asked what combinations of hamburgers and hot dogs provide the same level of satisfaction.
When these combinations are graphed, the slope of the resulting line is negative. This means that the consumer faces a diminishing marginal rate of substitution: The more hamburgers they have relative to hot dogs, the fewer hot dogs they are willing to consume. If the marginal rate of substitution of hamburgers for hot dogs is -2, then the individual would be willing to give up 2 hot dogs for every additional hamburger consumption.
The marginal rate of substitution has a few limitations. The main drawback is that it does not examine a combination of goods that a consumer would prefer more or less than another combination. This generally limits the analysis of MRS to two variables. Also, MRS does not necessarily examine marginal utility since it treats the utility of both comparable goods equally, though in actuality they may have varying utility.
Indifference curve analysis operates on a simple two-dimensional graph. Each axis represents one type of economic good. The consumer is indifferent between any of the combinations of goods represented by points on the indifference curve because these combinations provide the same level of utility to the consumer. You are not authenticated to view the full text of this chapter or article. Elgaronline requires a subscription or purchase to access the full text of books or journals.
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Now, the last thing I want to think about in this video is what the slope of this indifference curve tells us. When I talk about the slope, and this is really kind of an idea out of Calculus, 'cause we're used to thinking about slopes of lines.
So, if you give me a line like that, the slope is how much does my vertical axis change for every change in my horizontal axis? So, in a typical algebra class, that axis is your Y axis. That is your X axis. And when we think about slope, we say, okay, when I have a certain change in Y when I change in X by 1. So, we have something like this. So, when I change, I get a certain change in Y, the triangle means change in, delta, change in Y, when I get a certain change in X.
And delta Y, the change in Y, over change in X is equal to the slope. But this is when it's a line and the slope isn't changing. At any point on this line, if I do the same ratio between the change in Y and the change in X, I'm going to get the same value.
On a curve like this, the slope is constantly changing. So, what we really do, to figure out the slope exactly at a point, you can imagine, it's really the slope of the tangent line at that point. A line that would just touch at that point. So, for example, let's say that I draw a tangent line, I am going to draw my best attempt at drawing a tangent line and I'll do it in pink. Let's say I have a tangent line right from our starting predicament, just like that. And it looks something like that.
It looks something like that. And so, right where we are now, exactly at this point, you know, if we veer away, it seems like our slope is changing. Matter of fact, it definitely is changing.
It's becoming less steep as we go forward to the right. It's becoming more steep as we go to the left. But right there, the slope of the tangent line looks right like that or you can view that as the instantaneous slope right there. And we can measure the slope of the tangent line. We can say, look, if we want an extra, let's see, this looks like about, if we want an extra 2 pounds of fruit, how many bars are we going to have to give up?
How many bars are we going to have to give up? Well, it looks like we're going to have to give up, based on the slope right over there, looks like we're going to have to give up 5 bars. So, this is 5 and this is 2.
So, what is your change in, what is the slope here? The slope here, is going to be your change in bars, and I should actually say this is a negative right over there, it's going to be your change in bars, your change in chocolate bars, over your change in fruit. Over your change in fruit. And in this situation, it is -5 bars for every 2 fruit that you get. So, bars per fruit. Or you can say this is equal to So, it's essentially saying, exactly at that point, how are you willing to trade off bars for fruit?
Exactly at that point, it's gonna change, as things change along this curve. Now, it's going to be different. Once you have a lot more fruit, you're going to be much less willing to give up bars of chocolate.
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