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HELP PLEASE :)-- Economics THEORY OF THE FIRM (MC and ATC)
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 
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.
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!
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?
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
hhb777
I have another question if you don't mind: Why is profit maximised when MR=MC?
Because [total], so by definition, [marginal]. 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.
hhb777
But when MC=MR, wouldnt that mean that Marginal profit = 0?
Exactly, there is no more profit to be had.
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.
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.
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.
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.
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.
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.
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...
lol just read that your note at the end, ahh
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...
lol just read that your note at the end, ahh
lol just read that your note at the end, ahh
oh no i was just answering his second question about profit maximisation. And my quote was before your edit btw
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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