Question

For a monopolist, the unit cost of manufacturing a product is $3 and the demand equation is p= Va. What price will give the greatest profits?

299

likes
1494 views

Answer to a math question For a monopolist, the unit cost of manufacturing a product is $3 and the demand equation is p= Va. What price will give the greatest profits?

Expert avatar
Hester
4.8
116 Answers
Así es como se puede determinar el precio que generará la mayor ganancia para el monopolista: **1. Comprender los conceptos** * **Beneficio:** Ingresos totales menos costo total (Beneficio = TR - TC) * **Ecuación de demanda:** En este caso, la ecuación de demanda muestra una relación inversa entre el precio (p) y la cantidad demandada (implícita en 'a'). A medida que aumenta el precio, la cantidad demandada disminuye. * **Monopolista:** Un monopolista tiene el poder de fijar precios para maximizar sus ganancias. **2. Configurando las ecuaciones** * **Ingresos Totales (TR):** Precio (p) * Cantidad (q). Pero necesitamos expresar la cantidad en términos de precio usando la ecuación de la demanda. Como p = Va, podemos resolver para q: q = p/V * TR = p * (p/V) = p²/V * **Costo total (CT):** Costo unitario ($3) * Cantidad (q) * TC = 3q = 3(p/V) * **Ganancia:** * Beneficio = TR - TC = (p²/V) - (3p/V) **3. Encontrar el precio óptimo** Para maximizar las ganancias, un monopolista producirá donde el ingreso marginal (MR) sea igual al costo marginal (MC). Encontremos esos: * **Ingreso Marginal (MR):** La derivada de TR con respecto a p: MR = (2p/V) * **Costo Marginal (MC):** La derivada de TC con respecto a p: MC = (3 / V) **4. Ajuste MR = MC** * (2p/V) = (3/V) * 2p = 3 * p = 3/2 = $1.50 **5. Considerando la ecuación de la demanda** La ecuación de la demanda (p = Va) implica que 'V' es una constante que representa la pendiente de la curva de demanda. Necesitaremos el valor de 'V' para calcular un precio específico. Si V es muy pequeño, incluso el precio óptimo de 1,50 dólares puede no dar como resultado una ganancia positiva. **En resumen** * El precio de 1,50 dólares dará las mayores ganancias al monopolista, pero sólo si la curva de demanda permite una ganancia positiva dada la estructura de costos. Necesitará un valor para 'V' en la ecuación de demanda para obtener una respuesta más definitiva.

Frequently asked questions (FAQs)
What is the graph of the exponential function y = 2^x?
+
What is the length of the perpendicular bisector of a triangle, given that one side measures 10 units?
+
What is the volumetric formula for a cube?
+
New questions in Mathematics
Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps
two pails of different sizes contain 34.5 litres of water altogether When 0.68 litre of water is poured from the bigger pail into the smaller pail the amount of water in the bigger pail is 9 times that in the smaller pail. How much water was in the smaller pail at first?
How do you think the company has increased or decreased its income?
You have been hired to estimate the average weight of quarters in circulation. Based on the sample of quarters you collect (below), create a 90% confidence interval for the weight of quarters in circulation. Quarter Weights (grams) 5.631 5.714 5.719 5.689 5.551 5.723 5.705 5.627 5.627 5.715 5.576 5.632 5.641 5.676 5.660 5.699 5.609 5.634 5.713 5.591 5.674 5.675 5.684 5.694 5.655 5.632 5.598 5.675 5.628 5.562 5.636 5.583 5.567 5.551 5.649 5.708 5.696 5.614 5.637 5.601 5.628 5.711 5.566 5.653 5.653 5.597 5.687 5.717 5.678 5.654 5.556 5.707 5.563 5.628 5.679 5.714 5.555 5.719 5.634 5.647 5.717 5.612 5.705 5.657 5.670 5.607 5.687 5.666 5.612 5.718 5.714 5.713 5.663 5.641 5.589 5.656 5.712 5.639 5.577 5.580 5.674 5.636 5.625 5.597 5.616 5.591 5.616 5.700 5.706 5.695 5.562 5.699 5.607 5.573 5.659 5.632 5.654 5.568 5.628 5.687 5.605 5.689 5.687 5.554 5.618 5.701 5.681 5.645 5.714 5.665 5.661 5.634 5.714 5.586 5.656 5.673 5.657 5.717 5.611 5.578 5.579 5.614 5.644 5.724 5.647 5.566 5.697 5.558 5.586 5.586 5.611 5.573 5.573 5.709 5.629 5.649 5.552 5.615 5.645 5.611 5.686 5.588 5.641 5.704 5.703 5.696 5.557 5.551 5.725 5.608 5.725 5.603 5.677 5.638 5.573 5.640 5.561 5.631 5.563 5.671 5.662 5.569 5.648 5.680 5.681 5.551 5.555 5.578 5.701 5.645 5.670 5.574 5.594 5.705 5.633 5.719 5.680 5.647 5.641 5.553 5.616 5.698 5.552 5.566 5.559 5.697 5.686 5.560 5.629 5.701 5.622 5.615 5.553 5.608 5.637 5.663 5.696 5.714 5.675 5.613 5.594 5.669 5.569 5.716 5.705 5.603 5.709 5.717 5.606 5.581 5.575 5.601 5.600 5.664 5.715 5.705 5.583 5.586 5.592 5.550 5.628 5.662 5.603 5.559 5.676 5.558 5.678 5.671 5.642 5.581 5.568 5.706 5.665 5.712 5.574 5.602 5.699 5.716 5.693 5.711 5.635 5.612 BLANK #1: Is this a question involving mean or proportion? ***ANSWER "MEAN" OR "PROPORTION" (WITHOUT THE QUOTATION MARKS)*** BLANK #2: What is the LOW end of the estimate ***ANSWER TO 3 DECIMALS*** BLANK #3: What is the HIGH end of the estimate ***ANSWER TO 3 DECIMALS***
In a store, a person carries 14 kilos of rice and 28 kilos of flour. In what ratio are the kilos found? (Remember to simplify until you reach an irreducible fraction)
calculate the normal vector of line y = -0.75x + 3
The durability of a tire of a certain brand is a Normal random variable with an average of 64,000 km and a standard deviation of 9,000 km. Assuming independence between tires, what is the probability that the 4 tires on a car will last more than 58,000 km?
(24, -7) is on the terminal arm of an angle in standard position. Determine the exact values of the primary trigonometric functions.
The sum of two numbers is 144. Double the first number minus thrice the second number is equal to 63. Determine the first two numbers.
suppose random variable x follows poisson distribution with expected value 3. what is variance of x?
Buffalo Company makes and sells shampoo. Each unit requires $1.40 labor costs, material costs per unit are $0.90 and other variable costs are $0.30. It sells shampoo for $4.45 to retailers. Fixed costs are $15,000. It sold 25,000 units in the current month. What is the Break-Even point in units? What is the Break-Even point in dollars? What is the contribution margin of Buffalo Company?
Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.
7.57 Online communication. A study suggests that the average college student spends 10 hours per week communicating with others online. You believe that this is an underestimate and decide to collect your own sample for a hypothesis test. You randomly sample 60 students from your dorm and find that on average they spent 13.5 hours a week communicating with others online. A friend of yours, who offers to help you with the hypothesis test, comes up with the following set of hypotheses. Indicate any errors you see. H0 :x ̄<10hours HA : x ̄ > 13.5 hours
A diamond ring was reduced from $999.99 to $689.99. Find the percent reduction in the price. Round the answer to the nearest tenth of a percent, if necessary.
Determine the kinetic energy of a baseball whose mass is 100 grams and has a speed of 30 m/s.
A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.
Solve the following 9x - 9 - 6x = 5 + 8x - 9
For how long does the principal amount of €7,537 bring the same interest as the principal amount of €12,345 invested for 8 months? Interest calculation is simple and decursive.
question 1 Consider a sample space S, and two events A and B such that P(A ∩ B) = 0.2, P(A ∪ B) = 0.6, P(B ∪ ̄A) = 0.8 (a) [0.5 points] Calculate P (A). (b) [0.5 points] Calculate P (B)
Define excel and why we use it?