Time Series data and graph plotting

Question

The economists for Grant Corporation has established the company’s transportation using time series data to be

TC=50 16Q-2Q² 0.2Q³

A) Plot the curve for quantities 1 to 10 (Think u have to create ur own data here, idk)

B) Calculate the AVC and MC for these quantities and plot them another graph.

C) Discuss your results in terms of decreasing, constant and increasing Marginal Cost (MC).

Does Grant’s cost function illustrates all of these?

This is not my strenght so pls help!!

Is there any website I can use??

Answer 1

Ok, then results  will look something like this:

Q ...TC ....VC ....FC ...AVC ....ATC ....AFC ...MC(dq) MC(s)

1 ...64.2 ...14.2 ...50 ...14.2 ...64.20 ...50.00 ...12.6 ...14.2

2 ...75.6 ...25.6 ...50 ...12.8 ...37.80 ...25.00 ...10.4 ...11.4

3 ...85.4 ...35.4 ...50 ...11.8 ...28.47 ...16.67 .....9.4 ....9.8

4 ...94.8 ...44.8 ...50 ...11.2 ...23.70 ...12.50 .....9.6 ....9.4

5 ..105.0 ...55.0 ...50 ...11.0 ..21.00 ...10.00 ...11.0 ...10.2

6 ..117.2 ...67.2 ...50 ...11.2 ..19.53 ....8.33 ....13.6 ...12.2

7 ..132.6 ...82.6 ...50 ...11.8 ..18.94 ....7.14 ....17.4 ...15.4

8 ..152.4 ..102.4 ...50 ...12.8 ..19.05 ...6.25 .....22.4 ...19.8

9 ..177.8 ..127.8 ...50 ...14.2 ..19.76 ...5.56 .....28.6 ...25.4

10 .210.0 .160.0 ...50 ...16.0 ...21.00 ..5.00 .....36.0 ...32.2

MC(dq) means that marginal cost calculated using calculus method, but MC(s) means that marginal cost calculated using simple method MC(n)=TC(n)-TC(n-1).

MC is decreasing at range 0≤Q≤4 and then increasing at range 4<Q≤∞

But Danajaan did already analythical part.

Answer 2

A) I can't draw a graph here, but I can show you how to get the coordinates.  Since they ask you for Q=1-10, you just put each number from 1-10 in the function as follows:

Q=1, TC=50+16(1)-2(1)^2+.2(1)^3=64.2

B) AVC: First find the variable costs.  Variable costs are all those that depend on Q.  Everything in that function depends on Q except the 50, so TVC=16Q-2Q^2+.2Q^3.

To find AVC, simply divide TVC by Q.

AVC=16Q/Q-2Q^2/Q+.2Q^3/Q

AVC=16-2Q+.2Q^2

For MC, take the derivative of TC

MC=TC'=16-4Q+.6Q^2

C) We can find this information using the derivative of MC.  Where the derivative is negative, MC is decreasing; where the derivative is zero, MC is constant; where the derivative is positive, MC is increasing.

MC'=-2+1.2Q=0

1.2Q=2

Q=~1.67

So the derivative is zero at ~1.67.  This means that the firm has constant MC tangentially at that point.  Now we check to see how the function behaves above and below that point.

Q=1

-2+1.2(1)=-.8

The derivative is negative below 1.67, so MC is decreasing below 1.67.

Q=2

-2+1.2(2)=.4

The derivative is positive above 1.67, so MC is increasing above 1.67.

So yes, the cost function does exhibit all of these (though it's only constant at one point).