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# HELP PLEASE :)-- Economics THEORY OF THE FIRM (MC and ATC) watch

1. Can someone please explain to me why, on a short run cost diagram, Marginal Cost intersects Average Total Costs at its lowest point? I know its a mathematical relationship but i dont know what it is!! Any help is appreciated--Thank you
2. (Original post by hhb777)
Can someone please explain to me why, on a short run cost diagram, Marginal Cost intersects Average Total Costs at its lowest point? I know its a mathematical relationship but i dont know what it is!! Any help is appreciated--Thank you

Average cost is the cost that varies as production increases. As you increase production, marginal cost is the measurement of how variable costs change with each additional unit of production. If average cost is decreasing, the marginal cost for each additional unit of production is less than the average variable cost, but as soon as the average cost starts increasing the marginal cost (the cost of the next production level) crosses over and becomes higher than average variable costs.
3. Marginal cost is the cost of each extra unit. Average cost is the total cost divided by the number of units. If marginal cost is lower than average cost, then the average cost is falling (by definition, if you keep adding costs that are lower than the average, the average will fall). By the same principle, if marginal cost is higher than average cost, then the average cost is rising. Thus, the MC curve cuts the AC curve at its lowest point (the turning point). I hope that helps!

4. THANK YOU for your replies!! i thought noone would answer but haha you guys proved me wrong! anyway thanks, you guys really did help
5. (Original post by KiiNGofLONDON)
Marginal cost is the cost of each extra unit. Average cost is the total cost divided by the number of units. If marginal cost is lower than average cost, then the average cost is falling (by definition, if you keep adding costs that are lower than the average, the average will fall). By the same principle, if marginal cost is higher than average cost, then the average cost is rising. Thus, the MC curve cuts the AC curve at its lowest point (the turning point). I hope that helps!

I have another question if you don't mind: Why is profit maximised when MR=MC?
6. If you produce one more unit of output and your revenue increases by £10 and your costs increase by £5 then it makes sense to produce another unit of output. Say now revenue increases by £7 and costs increase by £6 then it still makes sense to produce another unit because you can make more profit. Now suppose you produce another unit of output and revenue increases by £5 but costs increase by £6. Clearly this last unit had a negative effect on total profits. Therefore you produce where the increase in revenue are equal to the increase in cost. i.e MR=MC
7. (Original post by hhb777)
I have another question if you don't mind: Why is profit maximised when MR=MC?
Because [total profit = total revenue - total cost], so by definition, [marginal profit = marginal revenue - marginal cost]. Total profit increases whenever marginal profit is positive (MR>MC), and falls whenever marginal profit is negative (MC>MR), so profit is maximised where MC=MR.

8. (Original post by KiiNGofLONDON)
Because [total profit = total revenue - total cost], so by definition, [marginal profit = marginal revenue - marginal cost]. Total profit increases whenever marginal profit is positive (MR>MC), and falls whenever marginal profit is negative (MC>MR), so profit is maximised where MC=MR.

But when MC=MR, wouldnt that mean that Marginal profit = 0?
9. (Original post by hhb777)
But when MC=MR, wouldnt that mean that Marginal profit = 0?
Exactly, there is no more profit to be had.
10. Unless your maths is good i would just take those relationships as they are, you wont need to know why for A levels anyways. Knowing why wont get you any more marks to be honest.
11. Want the mathematical proof? You will need to understand basic calculus... like quotient rule..

I'll give it to you anyway...

The total cost is a function of quantity: C(q)

Marginal Cost is the rate of change of cost with respect to quantity: mc = dC/Dq

Average cost = C(q)/q

therefore differentiating AC:

d(AC)/dq = 0 (zero gradient i.e. where MC cuts it)

[dC/Dq x q - C(q)] / q^2 = 0

dC/dq /q - C(q)/q^2 = 0 (remember dC/dq is MC) (now multiply throughout by q)

MC - AC = 0 MC=AC

QED.
12. (Original post by Srije)
Want the mathematical proof? You will need to understand basic calculus... like quotient rule..

I'll give it to you anyway...

The total cost is a function of quantity: C(q)

Marginal Cost is the rate of change of cost with respect to quantity: mc = dC/Dq

Average cost = C(q)/q

therefore differentiating AC:

d(AC)/dq = 0 (zero gradient i.e. where MC cuts it)

[dC/Dq x q - C(q)] / q^2 = 0

dC/dq /q - C(q)/q^2 = 0 (remember dC/dq is MC) (now multiply throughout by q)

MC - AC = 0 MC=AC

QED.
actually it can be done with basic calculus, this is from one of my previous posts.

You can prove it pretty simply with looking at profit, total cost and total revenue functions.

C= Cost
R=Revenue
T=total

Profit = TR-TC

The maximum point for Profit can be seen by finding the derivative of this equation and equaling it to 0.
dTR/dQ -dTC/dQ = 0

So happens that the first bit dTR/dQ = MR
and that dTC/dQ = MC

MR - MC = 0
Hence P Max at MC = MR

Btw i had my variable as being Q also, im not going to write up all the other functions (cant be bothered), this is just to show that mathematically it works out.
13. (Original post by yoyo462001)
actually it can be done with basic calculus, this is from one of my previous posts.

You can prove it pretty simply with looking at profit, total cost and total revenue functions.

C= Cost
R=Revenue
T=total

Profit = TR-TC

The maximum point for Profit can be seen by finding the derivative of this equation and equaling it to 0.
dTR/dQ -dTC/dQ = 0

So happens that the first bit dTR/dQ = MR
and that dTC/dQ = MC

MR - MC = 0
Hence P Max at MC = MR

Btw i had my variable as being Q also, im not going to write up all the other functions (cant be bothered), this is just to show that mathematically it works out.
Just reading your post quickly - it seems to prove P max is at MC=MR, how does this prove that MC cuts the ATC at its lowest point? The quantity at which profit is maximised is not necessarily the quantity where MC = ATC ... I'm sleepy so I could be missing something obvious forgive me if I'm wrong...

14. (Original post by Srije)
Just reading your post quickly - it seems to prove P max is at MC=MR, how does this prove that MC cuts the ATC at its lowest point? The quantity at which profit is maximised is not necessarily the quantity where MC = ATC ... I'm sleepy so I could be missing something obvious forgive me if I'm wrong...

oh no i was just answering his second question about profit maximisation. And my quote was before your edit btw
15. (Original post by yoyo462001)
oh no i was just answering his second question about profit maximisation. And my quote was before your edit btw
16. Or you can explain the ATC, MR/MC relationship with a different formula --> (1-ATC) x P i think, which would represent the profit a monopoly makes.
17. (Original post by hhb777)
I have another question if you don't mind: Why is profit maximised when MR=MC?
If MR > MC, then producing one more unit will cause an increase in profits. But if MR < MC, then producing one more unit will cause a decrease in profits. Hence the profit maximising output is MC = MR.

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