## To plot the curve for quantities 1 to 10, you need to substitute the values of Q into the total cost function and calculate the corresponding TC values.

a. Plotting the curve for quantities 1 to 10:

First, substitute the values of Q from 1 to 10 into the total cost function:

For Q = 1: TC = 50 + 16(1) - 2(1^2) + 0.2(1^3) = 64.2

For Q = 2: TC = 50 + 16(2) - 2(2^2) + 0.2(2^3) = 75.6

For Q = 3: TC = 50 + 16(3) - 2(3^2) + 0.2(3^3) = 88.2

For Q = 4: TC = 50 + 16(4) - 2(4^2) + 0.2(4^3) = 102.8

For Q = 5: TC = 50 + 16(5) - 2(5^2) + 0.2(5^3) = 119.2

For Q = 6: TC = 50 + 16(6) - 2(6^2) + 0.2(6^3) = 137.8

For Q = 7: TC = 50 + 16(7) - 2(7^2) + 0.2(7^3) = 158.4

For Q = 8: TC = 50 + 16(8) - 2(8^2) + 0.2(8^3) = 181.2

For Q = 9: TC = 50 + 16(9) - 2(9^2) + 0.2(9^3) = 206.8

For Q = 10: TC = 50 + 16(10) - 2(10^2) + 0.2(10^3) = 235.4

Plotting these calculated values for quantities 1 to 10 will give you the TC curve.

b. Calculating the average total cost (ATC), average variable cost (AVC), and marginal cost (MC):

To calculate ATC, divide TC by the quantity (Q).

To calculate AVC, subtract the total fixed cost (TFC) from TC and then divide by the quantity.

To calculate MC, find the change in TC for a one-unit increase in quantity.

For example, let's calculate these for Q = 10:

ATC = TC/Q = 235.4/10 = 23.54

AVC = (TC - TFC)/Q

Assuming the fixed cost is 100, TFC = 100:

AVC = (235.4 - 100)/10 = 13.54

MC = TC(Q) - TC(Q-1)

For Q = 10, TC(Q) = 235.4 and TC(Q-1) = 206.8 (Q = 9)

MC = 235.4 - 206.8 = 28.6

Repeat the above calculations for each quantity from 1 to 10 to get the values of ATC, AVC, and MC.

Plot these values on another graph.

c. Interpreting the results:

- If MC is decreasing, it means the cost of producing an additional unit is decreasing, which can indicate economies of scale or increased efficiency.

- If MC is constant, it means the cost of producing an additional unit remains the same, which could indicate constant returns to scale.

- If MC is increasing, it means the cost of producing an additional unit is increasing, indicating diseconomies of scale or inefficiency.

By looking at the MC values on the graph, you can determine the trend and whether marginal costs are decreasing, constant, or increasing.