Homework 11

Model

The information that we have been giving states that our current production rate is 20, our current total cost is $100 and our marginal cost is $7. With this information we can create an equation.

We use 20 which stands for units of production as an X value and cost which is $100 as a Y value.

F(x)=y, F(20)=$100 we know that function to be true now to create a formula we put that into a y=mx + b format plugging in 20 for x and 100 for y, this gives us 100=20m + b, our slope being our marginal cost which is the cost to produce 1 more unit, so our new equation looks like 100= 7(20) + b after we substitute 7 in. Now we solve for b which is,

100= 7(20) + b

100 = 140+b

100-140=b

-40 = b

So our final equation for this model is, y=7x - 40 if x≥20

Now we must find the cost to produce 150 flags using this model

we do this by plugging in 150 into x

y=7(150) -40

y=1050- 40

y= 1010, which is the cost to produce 150 flags using the model above.

Average cost of this model at 150 units

At the quantity of 150 flags we get the total cost to be $1010, to find the average cost of this we must divide $1010 by 150, when we do this we get that the average cost of each flag at this point in production is 6.74 which is higher than the average cost of the production of 20 flags which was an average cost of $5 per flag. So using this trend we can see that average cost increases as you produce more.

Other Models

-The average cost remains constant as production increases.

If we wanted to create a model which had a average cost remain the same them we would need a linear model with no B so when we try to get an average we always get the same outcome, so the model will look like y=mx, where m is any constant.

-For the average cost to remain constant to marginal cost must also remain constant a model that exemplifies this would be C(f)=MC where MC= Marginal

Cost. So, if MC=10 the formula will be C(f)=10(f). Now if flags increase by 10 products the formula will look like C(10)=10(10)=100, if it increases by C(20)=10(20)=200.

-The average cost diminishes as production increases.

We need to have a model which has a decreasing average cost as we increase the production so only way is to have a constant slope and no b value, we also need to make it so that as you increase the X value the Y value decreases. Thus this means that x and y are inversely proportional which is only attainable by having a situation which has y = m/x so as X increases and M stays the same we will get a smaller and smaller Y value.

-The average cost increases as production increases.

For this to happen we can not have a linear model, so it is not a linear model it must be a quadratic model which is can then be described as, y = x^a where a is any positive constant that remains the same for the specific model.

-You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

When one has an economy of scale that means that this company has an advantage at producing large number of quantities which thus lower its price at that range but when it comes down to small production its cost are quite larger. So for example we could have a company that for it to produce flags under a quantity of 600 flags its model would look like, y=7x-37 : x<600, but when it started producing at 600 or above it the cost of flags would be some thing fixed like, f(x) = 75 x≥ 600

-Any other interesting properties that you can think of and create a model for. Bonus points can be obtained for very interesting ideas.