Given Demand and Cost Functions Find level of output and price that maximizes Total Revenue

In this video we will try to solve a question on the revenue maximization of a firm. .we are given a demand function at a cost function and we were told to find the level of output and price which maximizes the total revenue.
The goal of the firm is to maximise profit. Therefore, the firm would be in equilibrium only when it achieves profit maximisation. The total revenue (TR) function of the firm gives its total revenue as a function of the quantity of output sold (q), i.e., TR = TR(q).
The total cost (TC) function of the firm, on the other hand, gives us total cost as a function of the quantity of output produced (q), i.e., TC = TC(q).
There are two conditions for profit maximization
FIRST ORDER CONDITION
That is, if the firm is to obtain maximum profit, it would have to equate its MR and MC, or, it would have to remain at the point of intersection between its MR and MC curves.
SECOND ORDER CONDITION
The first order or the necessary condition for maximum profit is also the first order or the necessary condition for minimum profit. That is why there should be an additional condition that should be satisfied along with the FOC. This condition is called the second order condition (SOC) or the sufficient condition for profit maximisation.
according to the SOC for maximum profit under perfect competition, the firm’s MC curve should be upward sloping towards right at the MR = MC point (where the FOC for maximum profit has been satisfied)
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[@Achola_Akoth]

Thank you so much....Am literally here and have an exams at 8..And can confidently say am good to go😊😊❤️

[@ECONMATHS]

Thanks for the appreciation dear.

[@rawrk4625]

YOUR VIDEOS ARE REALLY HELPING TO PREPARE FOR TOMORROW EXAM- THANKYOU SO MUCH MAY ALLAH BLESS U💗

[@immenselyharsh7435]

great work sir , please keep posting this type of problems,it just brushes numerical solving.

[@ECONMATHS]

Thanks for the appreciation. I ll try

[@darmukhtar1160]

Thank you for such wonderful explanation

[@lmatube7455]

It is the Best concept of Microeconomics Thank you for your contribution!

[@ECONMATHS]

thanks for the appreciation @lm@a tube

[@siomaihihi7685]

Im confused especially in the factoring/solving quadratic equation part. can you explain further sir?

[@parvaizhamid3703]

Thanks for this amazing video

[@Aesthetic-os9gd]

Sir you should also make playlist on macro economics.

[@brandinakaisala6553]

Thank you for your help Is Total revenue maximizing the same as profit maximizing??

[@gulammohd4164]

Great way of explaining complex things into simpler one

[@ECONMATHS]

Thanks for the appreciation

[@albertagbewoavi7966]

Nice presentation...I'm very grateful.♥️♥️🙌✌️💯

[@ECONMATHS]

@@albertagbewoavi7966thanks brother

[@user-zw5ut6he2j]

Quiz.calculate optimal output and prices given the demand and cost functions of a monipolist as; p=40+q and c=30+q^2

[@DebbieMyaYusuf1]

Thank u Sir hv really gained

[@ECONMATHS]

Thanks for the appreciation

[@estherwachira625]

I have loved this... thankful

[@ECONMATHS]

Thanks for the appreciation brother

[@maryngure5766]

Got it thanks 😊 But 24-16 is 8

[@danielmwale9730]

Good job, this is an eye opener for me

[@ECONMATHS]

Thanks for the appreciation brother

[@islamicstatus9462]

Thank you so much sir😊

[@2010Annie]

Do you have any video on when two firms have arrangement to collaborate by making decisions of production level together and how to determine the price and profit?

[@ECONMATHS]

No brother . If you have specific question on that topic I'll try to solve

[@tilahunenderasie4480]

THANKS!!!!

[@kamalsaid2333]

K=Q-Q²+Q³ k=capital Q=output derive supply curve when wk=1

[@alexwulugee6720]

Thanks!! Does this mean AC is the same as TC? What would graph of demand function be given Qd=-30p +0.05y +2Pr +4T when Y is 5000; Pr is 25; and T is 30

[@ECONMATHS]

I haven't mentioned that . The graph would be downward sloping with intercept the addition of last three terms of RHS

[@temboemmanuel3704]

suppose the cost function in a perfectlt competitive market os given by TC (Q) = 10 + 2Q2 and the market price is $40. a. determine the marginal cost. b. derive the total revenue and the profit functions. c. what level of output should be produced to maximise the profit? d. how much profit will be earned

[@mercyswtkiller6318]

Video was awesome thankyou

[@ECONMATHS]

Thanks for the appreciation

[@mirriamsakala8251]

Very helpful thank you How do you calculate profit from such a question ?

[@ECONMATHS]

Thanks for the appreciation. Max profit = TR -TC JUST PLUG THE VALUES.

[@tedharawa2348]

❤

[@emmanuelsarpong6523]

I learnt for maximization the value should be less than 0 eg. -4

[@VibranoteM]

Yes..u are right I also learnt that way

[@bezasemma3273]

Its great

[@alexwulugee6720]

Thanks, but could you help with this? Given a firm demand function Q-90+2p=0 and it's average cost function AC=Q2 -8Q+57+2/Q find the level of output which maximize total revenue

[@ECONMATHS]

I hope it will help kzbin.info/www/bejne/iZfdhIyDhJueZrc

[@qasemtv1737]

Thanks for the video it was educative, however 24-16 is 8 and not 9. And the Quadratic equation why didnt you use the formula.

[@elianquachelie7436]

I think what you are finding sir is the level output that maximizes profit rather than total revenue because at profit maximization MR=MC

[@ECONMATHS]

Sorry I couldn't saw your comment. You are right. Itz profit maximization problem

[@ameetkumar3178]

Other new problems kindly upload

[@ishasah6292]

sir, is this same as profit maximization?

[@leonardhakizimana3696]

Why MC is a horizontal line while it’s equation looks like is not?

[@economicthought53]

Sir .please clear my doubt.The question is not to find the profit maximising output.It is to find the revenue maximising output.If so,MR becomes zero when TR maximises

[@ECONMATHS]

You are absolutely right. My mistake

[@vhinxtapz9479]

sir how about Q=100-2P TC= Q³-10Q²+10Q+5 how to derive profit function?.:(

[@ukpenignatiusigbawase1931]

Please Sir, could you help solve problem for me, this is two weeks with it, yet no understanding. A firm's average cost function is given by Y=x²-20x+120 where Y is average cost in naira per unit of output and output price is N10 and is same at all levels. 1. Find the output levels at which the firm breaks even(i.e price=average cost) 2. Graph the cost function and show solution 3. Find a range of prices over which the firm makes across at all levels of output

[@ECONMATHS]

Did i SOLVED this question?

[@2010Annie]

Please, this is very urgent. How did you arrive at Q to the power of 2 -5Q+4=0

[@ECONMATHS]

3Q² -15Q+12=0 3(Q²-5Q+4)=0 (Q²-5Q+4)=0/3 Q²-5Q+4=0 I hope this helps

[@2010Annie]

@@ECONMATHS. Yes. It did

[@cherutichcaren3226]

Thanks alot but can you please do this👇👇 Given c=36+(Q-8)²where c is the MC of producing Q units and R=100-2Q where R is the MR os selling Q units Required a. Determine the profit maximizing output of the firm b. Derive the equation for TC and TR c. What's the value of the maximum profits

[@ameetkumar3178]

Thx sr🎉

[@ECONMATHS]

Welcome

[@francismali5840]

I'm a bit lost???🤔🤔 Q=1 was maximizing the profit function What about maximizing the total revenue????? Why finding the second derivative of the mc only???? Instead the profit maximisation equation?

[@maxwellntambo3909]

Thank you sir for this precise explanation. Help me solve: given price as P=63-Q and the supply curve is given to be P=30+2Q 1. Draw the market demand and supply curves 2. Calculate elasticity of demand at the following prices; p=24, p=20, p=20. 3. Explain how the Market equilibrium changes of government increased peoples income which shifts the curve by 20? I will be grateful sir

[@commercelecturewithashfaque]

Wait let me confirm I think than there will be derivative of equation than further calculation

[@kasegujesero7062]

Thank you alot

[@ECONMATHS]

My pleasure

[@dharshisara4725]

Sir how to calculate tvc and avc ????

[@prosper2047]

Please I have a question to….. Assuming a price function is given as: P = 180-40 and a cost function as: C=20+ find profit maximizing output and price also determine whether total profit is maximum at the output obtained based on the first and second order condition of profit maximization.

[@ECONMATHS]

Cost function?

[@emmanuelsarpong6523]

And also the question asked to find the level of output and price at which TR are maximized . Buh you only found the maximizing output but you didn’t find the price So should we insert 1 or 4 to get price ?

[@alankritagupta9544]

A price taking firm has a cubic total cost function given by; C =.04q^3-.09q^2+10q+5 (a) If market price of output is Rs. 4 per unit, what is the profit maximizing amount of output? (b) What is the firm’s profit at this price? (c) What would be its loss if discontinued production? Plz solve this question sir!

[@aryanshpratapsingh2811]

Can we solve it by TR minus TC aporoach

[@2010Annie]

Is optimal value of production same as OUTPUT?

[@ECONMATHS]

Yes

[@maryngure5766]

How is price maximized ????

[@amitvishwakarma6208]

Consider A Firm facing the demand schedule P = 190 - 0.6q and the total cost function TC = 40 + 30q + 0.4q2 a) What output will maximize profit? (5) b) What output will maximize total revenue? (3) c) What will the output if the firm makes the profit of Rs. 4,760 Yeh solve kar dijiye plz

[@shitijjindal6157]

Sir thanks for this concepts But can you solve one question for me? Demand function Q=100-2P MC=AC=10 What is maximum profit at equilibrium level??

[@ECONMATHS]

Solved the question

[@ECONMATHS]

Check the latest video

[@shitijjindal6157]

@@ECONMATHS ok sir can you tell me from where you are sir?

[@ECONMATHS]

I am from Kashmir

[@samsonkarugu423]

can you solve p=6-1/2q

[@amitvishwakarma6208]

Consider A Firm facing the demand schedule P = 190 - 0.6q and the total cost function TC = 40 + 30q + 0.4q2 a) What output will maximize profit? (5) b) What output will maximize total revenue? (3) c) What will the output if the firm makes the profit of Rs. 4,760 Yes solve kar dijiye plz

[@moseskiputa6837]

24 - 16 is 8 though.

[@ECONMATHS]

Can happen

[@Payeex]

Can you solve a multiple output cost function

[@ECONMATHS]

Can you have a specific question please

[@ruthsawe5261]

Have a question can I ask sir?

[@ECONMATHS]

Sorry brother I couldn't saw your comment earlier

[@marandaeguosa144]

Please , kindly solve this problem: Given the demand and cost function of a firm, p=10-q and c=15+2q respectively, find the largest quantity that is consistent with (1) break even (2) making profit of $10 and making loss of $20.

[@ECONMATHS]

I ll but as I told earlier , I have some health issue . Lete recover first

[@marandaeguosa144]

@@ECONMATHS please take good care of yourself, hope you recover soonest.

[@kesiimeritah5992]

please help me out with this TC=0.04Q^3_0.9Q^2+10Q+5 find FC VC AC AFC AVC AMC

[@AkashDeep-ml9py]

Why have you equate MR and MC and.... then check for the slope of MC~?? Why don't you just find MR then equate it to zero ......then check double differentiation at that point....if

[@ECONMATHS]

To make it relatable with graph I did this . Otherwise the are other methods also to check SOC . Can't we take second derivative of mc at critical point and check it's sign? I only didn't it more understandable . If you find mistake please notify me. I'll love to be rectified

[@AkashDeep-ml9py]

@@ECONMATHS but if we follow that step(that i have mentioned above)...the value of Q(where MR =0 MR'

[@ECONMATHS]

@@AkashDeep-ml9py are you are saying that equilibrium output will be 45? . If thatz the case then put q= 45 in profit function ie TR- Tc ,

[@AkashDeep-ml9py]

@@ECONMATHS yaa.....i know that will not be maxm....but in question we are asked to maximize revenue(P.Q)....not profit(TR-TC)

[@AkashDeep-ml9py]

If it was asked to maximize profit then Q=4 is absolutely right....but there is to maximize Revenue🙄

[@rihanakhan1128]

Sir I have doubt ..may be I am wrong but according me TR is maximum where MR =0, so if I put MR =0 according this question MR=45-.5×2Q=0 then Q=45 ...please correct me if I am wrong . I am here not to prove u wrong but I am confused ...please accept my request and clear my confusion

[@ECONMATHS]

And corresponding to q= 45 MC =3×45×45-(16×45)+2=5357 And MR= 45 Think about this way

[@rihanakhan1128]

@@ECONMATHS here is one more doubt related this ,please correct me .. In case of profile maximization we put MR=MC ,from this we can get the level of output where producer can maximize his profit When we talk about revenue maximization we put MR =0 because at this level TR is maximum Here my point is when question ask about profile maximization we should put MR=MC to find out level of output and when question Is about revenue maximization we should use MC=0 to get level of output ...because I think both conditions are for different situation..we can't say when profit is maximum , revenue is also maximum at that point ..because if I say revenue is maximum means MR =0 , and according you if I put MR=MC at this point my MC=0 which is not correct and I can't deny that TR is always maximum when MR=0 ...here is my view and I really want your clarification about this ...I would be grateful if u reply me sir

[@MelesseShemuye-tr2fe]

24_16 is not 9 but 8

[@juzi1893]

24 minus 16 is 8

[@ECONMATHS]

Yes

[@user-yi2wx7ql1r]

You're giving us a wrong total revenue

[@reathtutmalou3982]

Hi! Please help me solve this question. .Suppose the firm operates in a perfectly competitive market. The market price of his product is 10$. The firm estimates it's cost production with the following cost function: TC=2+10Q-4Q^2+Q^3 a) What level of output should the firm produce to maximize its profit? b)Determine the level of profit at equilibrium. c)What minimum price is required by the firm to stay in the market?

[@ECONMATHS]

Uploading

[@ECONMATHS]

Uploaded

[@glop7459]

Sorry but Not good one to me