# 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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241 shows that a firm is actively participating in a purely competitive industry where the price and minimum average total cost are equal to \$50. Also, the figure shows that economic profits are zero, meaning that the industry is resting at its original equilibrium and has no reason for other firms to enter or leave the competition. For this reason, the existing firms in pure competition are earning normal profits which means that accounting profits are equal to owners of each firm will earn on…

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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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New Balance is moving into a toning market with a pair of attractive shoes that has hidden balance technology. The purpose is to present, “Why walk when you can tone your body”, when you’re simply just walking or even doing your everyday chores. True Balance shoes promises 29% muscle activation and 10% calorie burn. Many women are getting intrigued with the idea of losing weight by these shoes from the percentages, but what if they percentages were lower. Would you still buy them? Even though,…

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Francisco Gutierrez 03.03 Linear Functions 1. The equation we have is 2x+3y=1200. The first thing you would need to do in the equation is subtract 2x to both sides. 2x cancels out and now we subtract 2x and 1200. You would end up getting 3y=2x-1200. Then finally, you would have to divide everything by -3. Your final answer for this question is y=-2/3x+400. Your slope is -2/3 and your y-intercept is 400. 2. So we know that our slope is -2/3 and the y-intercept is 400. You have one point on the…

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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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