We are covering average total and variable cost curves in class. What I am wondering is:
thanks in advance
Dustin
Hey! Nice to have you here.
I am not an expert in this and I'm just learning it, but here is what I understand. Hopefully someone can correct me if I'm wrong.
1) I don't think their intersection points would be meaningful. Their shapes would also not be important just by themselves.
2) Nothing significant about that.
Now, to explain why.
Right now, you're probably taking principles of microeconomics. If you take inermediate Micro, then you will learn how the curves are constructed and how the neoclassical firm works.
Before I go into a long explanation, are you comfortable with calculus?
What do you mean by "individual variable costs"?
Where MC changes directions is only significant because of decreasing marginal returns. Cost per unit starts increasing instead of decreasing as gains from specialization dissipate.
thanks for the response. you are correct that it is principles of microeconomics, I took macro last semester. I was questioning the thought of using each individual cost so as to view the greatest "offender"/contributor to the variable cost curve; what is the cost that should be focused on to reduce.
I am a few weeks away from finishing precalculus and we have touched on some calculus material, and I have completed stats 1 and 2, but if your willing to explain, I will do what is necessary to figure it out.
What I mean by individual variable costs is the cost of the individual factors rather than their total. Also, I was thinking of it being graphed with the mc, atc, and avc. Since you could see each curve, you can see how they contribute to the avc.
In the neoclassical framework, there is a function which describes the maximum (optimal) level of output given various levels of input.
For example, you can have Q = 10K0.4L0.6
This function describes how your output changes for a change in your capital (K) and your labor (L).
We'd like to be able to graph this function, yet it's in three dimensions, so instead we have a construct called an isoquant. An isoquant is a description of all the various combinations of inputs you can have to produce a fixed level of output. For example,
Look only at the curve itself. The dashed lines are just for explanation.
This curve describes all the combinations of Factor Y and Factor X that can produce a given quantity of product, say q.
Notice that the more of one factor we give up, the more of the other we will need. For example, start where Factor X is 5, and move left. As we give up 1 unit of X, we need to gain 1 unit of Y. But for the next unit of X we give up, we need to gain 2 of Y. This shows that the factors of production have some property of mixing together, and that if we are running too low on one, we will need to overcompensate with the other (in a non-linear fashion oftentimes).
Now, you can draw many isoquants that correspond to various levels of production:
Now we ask the question "where should the firm produce?" To answer that question, we need to know not only the productivity of the factors, but also their price.
If the price of labor is w, the price of capital is r, and the fixed costs are f, then the total costs of production will be
TC = wL + rK + f
If you draw this out on a graph, you get
The point is, it's a linear equation that slopes down. Depending on the total cost, there are multiple isocost curves, all of which have the same slope.
For a given total cost, you have one specific isocost curve. The isocost curve represents all combinations of inputs you can use that cost the same amount.
Now, when you are given a specific cost, you can combine the isocost curve with the isoquant curve. Say you have one specific cost curve. Now you have to decide at which point to produce:
You have the cost curve which is the straight line, and various isoquant curves which are curved. Notice that the quantity produced for each isoquant increases in the North-Eastern direction. Each isoquant which is above the other is a greater production.
So which isoquant do you use? Well, if we use the lowest one, that intersects the cost curve, right? Both at point x and at point z. However, is this the maximum production you can achieve? No. The next isoquant up (the middle one) intersects the cost curve as well (meaning the same cost), but has higher production (because it's above the lower one). The last isoquant (the top one) is unreachable, because it is too expensive.
How do you solve this mathematically?
Well, we need to go back to the isoquant curve first. The isoquant curve has a slope, which is called the Marginal Rate of Technical Substitution*. When the two factors we're looking at are capital and labor, the slope is (change in capital)/(change in labor). That is, for every change in labor of 1 unit, how much does capital change? Look at the isoquant curve I first showed. The further right you go, the more labor you add, one by one. The slope of the isoquant decreases (in absolute value), which means that every gain of one unit of labor can replace less and less capital (meaning it's more difficult to replace that capital).
The point is, the slope is the MRTS. If you use calculus, you write MRTS = dK/dL.
So how you do find an expression for the MRTS? Well, if you are given a production function, Q = 10K0.4L0.6, you can calculate the marginal product of labor and the marginal product of capital. The marginal product of capital is dQ/dK, which means "by how much production will change for a small change in capital." The MP of labor is analogous. You can find the MP of labor and capital by taking the partial derivative of the production function with respect to the variable you want. For example, if you want to find the MPK, what this does is ask "how does Q change when K changes, given that L is constant". Notice that MRTS = (change in capital)/(change in labor), right? Well, that is dK/dL. How can we calculate dK/dL from the individual MPs? Well, if we do MPL/MPK, we will get (dQ/dL)/(dQ/dK), which, after some fraction algebra cancels the dQ term and gives you dK/dL, which we wanted. Hence, we get a way of finding MRTS for a given production function.
Now, notice that when the isoquant and isocost lines meet at the optimal level, their slopes are equal (and they are tangent to each other). The slope of the isocost line is (price of labor)/(price of capital), or w/r.
To solve the equations, we need to set the slopes of the two curves to be equal:
PL/PK = MPL/MPK
This will give us the point at which they meet just right.
So we see that the place that matters is where the ratio of the prices equals the ratio of the Marginal Products.
To see why this makes sense, rearrange the equation and put it as MPL/PL = MPK/PK. What that means is that the marginal productivity of labor per dollar cost of labor is equal to the marginal productivity of capital for dollar of capital. This is very important, because if the left side of the equation were less than the right side, that means that you can squeeze more productivity out of capital for every dollar (at the current rate of production), and hence you should use more capital and less labor. As you replace the labor, then, the two sides become more and more equal.
* The MRTS is actually the absolute value of the slope (the slope is negative).
Yea, that. NBD n' stuff.
You should read what I wrote, Neodoxy - it's intermediate Micro in a nutshell. That's literally 1/3 of the course.
The first third is consumer preferences (where the situation is very similar, only you have indifference curves instead of isoquants and budget constraints instead of isocost lines).
The last third... I am not yet sure. Haven't taken the last third yet :P
Yea, I actually saved it.
Michelangelo - your answer to #2 is incorrect - economies vs diseconomies are related to Average costs, not marginal costs.
Thanks so much for the response. I have some research to do but I would like to make sense of this. Perhaps its only on my end, but the last two pics didn't show up on the post.
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