The economist for the Grand Corporation has estimated the company’s cost function, using the times series data to be

TC=50+16Q-2Q2+0.2Q3
a. Plot this curve for quanties 1 to 10
b. Calculate the average total cost, average variable cost and marginal cost for these quanties, and plot them on another graph.
c. Discuss your results in terms of decreasing, constant and increasing marginal cost. Does Grand cost function illustrate all theses.

your question is??

To answer these questions, we will need to follow a step-by-step process:

a. Plotting the cost curve for quantities 1 to 10:
To plot the cost curve, we will substitute different values of Q (quantities) into the cost function TC=50+16Q-2Q2+0.2Q3. Here are the calculations for quantities 1 to 10:

For Q = 1: TC = 50 + 16(1) - 2(1)^2 + 0.2(1)^3 = 63.2
For Q = 2: TC = 50 + 16(2) - 2(2)^2 + 0.2(2)^3 = 68.8
For Q = 3: TC = 50 + 16(3) - 2(3)^2 + 0.2(3)^3 = 69.6
...
And so on until Q = 10.

Plotting these points on a graph will show the shape of the cost curve for quantities 1 to 10.

b. Calculating and plotting the average total cost, average variable cost, and marginal cost:
To calculate the average total cost (ATC), average variable cost (AVC), and marginal cost (MC) for each quantity, we need to use the following formulas:

ATC = TC / Q
AVC = TVC / Q (where TVC is total variable cost)
MC = ΔTC / ΔQ (change in total cost divided by change in quantity)

We can use the cost function TC=50+16Q-2Q2+0.2Q3 to calculate these values for each quantity, and then plot them on another graph.

c. Analyzing the results in terms of decreasing, constant, and increasing marginal cost:
To determine if the cost function illustrates decreasing, constant, or increasing marginal cost, we need to examine the values of MC calculated in step b.

If MC decreases as quantity increases, it indicates decreasing marginal cost.
If MC remains constant as quantity increases, it indicates constant marginal cost.
If MC increases as quantity increases, it indicates increasing marginal cost.

By analyzing the values of MC calculated for each quantity, we can determine if the Grand Corporation's cost function illustrates any of these.