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.
a. To plot the cost curve for quantities 1 to 10, we can use the cost function provided:
TC = 50 + 16Q - 2Q^2 + 0.2Q^3
Let's substitute the values of Q from 1 to 10 into the cost function to find the total cost (TC) for each quantity. Then, we can plot these points on a graph.
For Q = 1:
TC = 50 + 16(1) - 2(1^2) + 0.2(1^3) = 64.8
For Q = 2:
TC = 50 + 16(2) - 2(2^2) + 0.2(2^3) = 81.2
For Q = 3:
TC = 50 + 16(3) - 2(3^2) + 0.2(3^3) = 98.4
Continue this process for the remaining quantities up to Q = 10.
Once you have all the TC values for quantities 1 to 10, you can plot them on a graph.
b. To calculate the average total cost (ATC), average variable cost (AVC), and marginal cost (MC) for these quantities, we can use the following formulas:
ATC = TC / Q
AVC = TVC / Q
MC = ΔTC / ΔQ
Where:
TC is the total cost
Q is the quantity
TVC is the total variable cost
ΔTC is the change in total cost
ΔQ is the change in quantity
Now, let's calculate the ATC, AVC, and MC for each quantity from 1 to 10.
For Q = 1:
TC = 64.8
ATC = 64.8 / 1 = 64.8
AVC = TVC / 1 (in this case, AVC = TC because there are no fixed costs)
MC = ΔTC / ΔQ (MC will be calculated for each pair of consecutive quantities)
For Q = 2:
TC = 81.2
ATC = 81.2 / 2 = 40.6
AVC = TVC / 2 (in this case, AVC = TC / 2)
MC = ΔTC / ΔQ
Continue this process for the remaining quantities up to Q = 10.
Once you have the ATC, AVC, and MC values for each quantity, you can plot them on a separate graph.
c. Discussing the results in terms of decreasing, constant, and increasing marginal cost requires analyzing the values of MC.
If MC is decreasing, it means that producing one more unit of output is becoming cheaper, indicating economies of scale.
If MC is constant, it means that producing one more unit of output costs the same as the previous unit, indicating constant returns to scale.
If MC is increasing, it means that producing one more unit of output is becoming more expensive, indicating diseconomies of scale.
By comparing the MC values obtained from the cost function, you can determine whether the Grand Corporation's cost function illustrates decreasing, constant, or increasing marginal cost.
To answer this question, we need to understand the terms and calculations involved. Let's break it down step by step.
a. Plotting the cost curve for quantities 1 to 10:
To plot the cost curve, we will substitute the values of Q (quantity) from 1 to 10 into the cost function TC = 50 + 16Q - 2Q^2 + 0.2Q^3. The resulting cost values will be plotted on the y-axis, while the corresponding quantities will be plotted on the x-axis.
b. Calculating average total cost (ATC), average variable cost (AVC), and marginal cost (MC):
1. Average total cost (ATC) is the total cost (TC) divided by the quantity (Q). To calculate ATC, divide the cost function TC by Q.
ATC = TC/Q
2. Average variable cost (AVC) is the variable cost (VC) divided by the quantity (Q). To calculate AVC, subtract the fixed cost (FC) from TC and then divide by Q.
AVC = (TC - FC)/Q
3. Marginal cost (MC) is the change in total cost (TC) due to a change in quantity (Q). To calculate MC, take the derivative of the cost function TC with respect to Q.
MC = d(TC)/d(Q)
For each quantity from 1 to 10, calculate the corresponding ATC, AVC, and MC using the formulas above.
c. Discussing the results in terms of decreasing, constant, and increasing marginal cost:
Marginal cost (MC) indicates the change in the total cost resulting from a change in quantity. If MC is decreasing, it means the additional cost of producing one more unit is decreasing. If MC is constant, it means the additional cost remains the same for each additional unit. If MC is increasing, it means the additional cost of producing one more unit is increasing.
By analyzing the results obtained in step b, discuss whether the Grand Corporation's cost function illustrates decreasing, constant, and increasing marginal cost.
Now, let's go ahead and calculate and plot the curves to find the answers to the questions.