Economics 8

Q = 800 − 0.25P

P = 3,200 − 4Q

TR = P × Q = 3,200Q − 4Q 2

MR = DTR/DQ = 3,200 − 8Q

Therefore, the slope of the curve is −8.

Help me in understanding the solution. I did not understand the steps.
Question is to calculate the slope of the marginal curve.
i understood it till TR=P x Q . After that in did not understand how did they move forward.

If I understand you correctly, you understand how to get the TR equation which is simply P×Q above:
(3200 - 4Q)(Q) = 3200Q - 4Q^2

The MR equation is calculated as the first derivative of that above equation. To take the first derivative you remove the Q from the 3200 and multiply the 4 by the 2 after the Q. If you’re unfamiliar with first derivatives you can find a quick primer on YouTube that can sort you out fast. Math on CFA won’t be too complex but knowing how to do the first and second derivatives of things can be very useful. In any case MR is the first derivative of the TR equation and equals:
3200 - 8Q.

-8 is the output slope of that MR equation. That’s where it comes from.

Cheers - good luck - you got this👍

Thank you so much for helping :yellow_heart:. But can you help in how to calculate the first deviation of TR

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Here is how I did it above. Cheers - good luck - you got this👍

If f(x) = x^n where n is a constant, then f’(x) (notation for first derivative) = n * x ^ (n-1).

It’s a calculus thing. :man_shrugging: :nerd_face:

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Thank you so much. It’s really helpful :tulip::heartpulse:

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Thank you so much for help. Gratitude :tulip::heartpulse:

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