# Inverse demand function

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C(Q1)=8(q1)2 → MC1=16q1 C(Q2)=10(q2) → MC2=10 P=(150-4q2)-4q1 → Using double slope rule find MR1 → P=(150-4q2)-8q1 P=(150-4q1)-4q2 → Using double slope rule find MR2 → P=(150-4q1)-8q2 Set MR=MC to find best response function for each firm Reaction 1: P=150- 8q1-4q2=16q1 q1=6.25-1/6q2 Reaction 2: P=150-4q1-8q2=10 q2= 17.5-1/2q1 B. Cournot Nash Equilibrium price =\$72.72 Cournot Nash Equiiibrium quantity= 3.63+15.68 → 20.63 C(Q1)=8(q1)2 → AC1=8(q1)2/q1 → AC1=8q1 C(Q2)=10q2 → AC2=10 q1=3.636; q2=15.685 1= P*q1 - AC*q1 → =(150-4(q1+q2))*q1)-(8q1*q1) → =150q1-12q12-4q1q2 → plugging in→ Firm 1 profit: 1=\$158.68 2= P*q2 - AC*q2 → 150q2-4q22-4q1q2-(10*q2) → Firm 2 profit: 2=\$983.68 C.Stackelberg: Find Follower's best response “Firm 1: ”P=150-4q2-4q1 → MR1=150-4q2-8q1 MC=16q1 → Set MC=MR → 150-4q2-8q1=16q1 → q1=6.25-(1/6q2) → Substitute Follower’s best response into market demand function → P=150-4q2-4q1 → P= 150-4q2-4(6.25-(1/6q2)) → P=125-3.333q2 Leader uses this to maximize own profit → solve for leader's best response → MR2=125-6.666q2 → Set MR2=MC2 → 125-6.666q2=10 → solving for q2 → q2=17.25 is the leader's profit maximizing quantity to produce → 6.25-(⅙(q2)=q1 → 6.25-2.875=q1 → q1=3.375 → Q=3.375+17.25 → Q= 20.625 → sub back into demand function → =150-4(20.625) → P=\$67.5 is the Stacklberg price 1= P*q1 - AC*q1 → =(150-4(q1+q2))*q1)-(8q1*q1) → =150q1-12q12-4q1q2 → plugging in→ 1=\$136.69 2= P*q2 - AC*q2 → 150q2-4q22-4q1q2-(10*q2) → Firm 2 profit: 2=\$991.9…

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Derived demand for labor depends on the market value or product price of the good or service (McConnell, Brue, & Flynn, 2011). The demand for labor depends on productivity of the market value of goods produced (McConnell, Brue, & Flynn, 2011). The production of products is done by laborers, or the labor demand, and the derived demand is from the demanded product that is done by the same laborers. The concept helps determine the demand for the labor of specific goods, what is needed, how much is…

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Inverse Functions of Trigonometric Functions As high schoolers go their their teenage years of high school they learn from a variety of subjects. From math to science to history, there is a depth of knowledge to be learned. For math 3 and math 4, we are introduced to the world of trigonometry. So far, we have learned that there are currently three main trigonometric functions, cosine, sine, and tangent. But today I want to explore the other side of the trigonometric world, the inverse…

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accessory. Maxim expects that demand will be slow at first but will pick up quickly as automobile accessory stores begin to stock the product and as word-of-mouth promotion spreads awareness. Maxim also plans to produce a humorous video for posting to YouTube and to utilize social-media marketing to spread awareness and enthusiasm for the new product. Market demand estimates provided by Maxim are that the firm expects to sell about 125,000 units into the U.S. market within 24 months, and that…

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the problem given to them and their reasoning for this answer. In essence, I was hoping to target students’ knowledge of inverse functions and how they applied it to solving a situational problem. More specifically, if they were able to find the error in a solution of an inverse algebraic problem and explain their reasoning for this error. Moreover, once a student was able to state their response, I questioned their thinking and reasoning behind it in the hopes that they would use their prior…

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Fundamental Theorem of Calculus The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of…

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John Gutmann was one of America’s most distinctive photographers. Gutmann was born in Germany where he became an artist. He later fled Germany due to the Nazi’s because he was a Jew. Gutmann moved to San Francisco and re-established himself as a photojournalist captivating the lives of Americans. He mainly took photographs of people who were imperfect like himself because of his Jewish nationality. Gutmann targeted the poor, circus folk, the gay community and the rich. Two of Gutmann’s works are…

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The fundamental theorem of Calculus: The fundamental theorem of calculus asserts the interrelated properties of integration and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation. First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows, A(x)=∫_c^x▒f(x)dt, if a≤x≤b.…

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the equation & based off what I did I'm assuming that his possible answer came out not to be an real answer to his problem & that is mainly because the equation itself is not true when eighty one is inserted for the letter x in the default problem. Okay so basically for this particular problem we have to think of f of x as basically the y value if that makes sense. So this would mean that if you use addition for the number two & + to the letter y we will see the function go up by two. The…

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Story evaluation The story that will be evaluated is one entitled “Man was paid \$2 500 to conceive a child with his neighbor’s beauty queen wife, but failed after 3 months trying”. Firstly, there is doubt in the story due to the source which is responsible for sharing the news. The source is a website known as 9GAG, which does not have any reputable evaluation system, and anyone is free to post a story he or she wants. However, judging by the comments on the post, many individuals assume the…

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