2.The marginal revenue of a firm is given by the following equation: MR(Q) = 22 +21Q + 16Q2 Where, Q represents the quantity produced. Also given, the total revenue of the firm, when they produce 5 units of output, is 50, i.e., TR(5) = 50. Calculate the firm's total revenue function. What is the value of the constant term in the total revenue function? Answer in two decimal places. Be careful about the sign. Calculate the total revenue of the firm when the firm produces 7 units of output. Answer in two decimal places.
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- Question 1: Given the following cost function:TC = 1500 + 15Q – 6Q2 + Q3i. Determine the total fixed cost for producing 1000 units of output and 500 units of output.ii. What is AFC at:a) 1000 units of outputb) 500 units of outputiii. Determine TVC, AVC, MC and AC at 50 units of output. Question 2: The demand function equation faced by PTCL for its computers is given by:P = 50,000 – 4Qi. Write the marginal revenue equationii. At what price and quantity marginal revenue will be zero?iii. At what price and quantity will total revenue be maximized? Question 3: Suppose the following demand and supply function:Qd = 750 – 25PQs = -300 + 20 Pi. Find equilibrium price and quantityii. Find consumer and producer surplus Question 4: Given production function:Q = L 3/4 . K1/4Find out the optimal quantities of the two factors using Lagrangian method, if it is given that price of labor is Rs.6 and price of capital is Rs.3 and total cost is equal to Rs.120.Question 5: Given the cost function isTC = 6L…Mathematics for Business and Economics Q1) 3x2 ( 12x3 + 20 )0.5 within the range 6 and 8. Q2) The marginal revenue of a firm is given by the following equation: MR(Q) = 20 + 14Q + 13Q2 Where, Q represents the quantity produced. Also given, the total revenue of the firm, when they produce 5 units of output, is 50, i.e., TR(5) = 50. a)Calculate the firm's total revenue function. What is the value of the constant term in the total revenue function? b)Calculate the total revenue of the firm when the firm produces 7 units of output.2. ABC Manufacturing has provided you with their demand function Qd = 2000-2p and supply function Qs = 60+5p, please answer the following questions: a. What is the company’s marginal revenue function? b. At level of output is profits maximized? c. At what price is profits maximized? d. What is total revenue at the profit maximization level of output?
- The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) =1/30 q2 − 12.85q + 20 + 400/q, where q is the firm's output. i. Is the rate of change of profit increasing or decreasing when theouput level of the firm is 10 units?ii. Determine the level of output for which the firmᇱs profit is maximized.iii. What is the firm's maximum profit?The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q + 20 +400/q, where q is the firm's output. i. Is the rate of change of profit increasing or decreasing when theouput level of the firm is 10 units?ii. Determine the level of output for which the firm's profit is maximized.iii. What is the firm's maximum profit?Faye is an entrepreneur considering whether to enter the market for providing websites to universities offering online learning. The market is currently perfectly competitive, and the market-clearing price is $10,000 per client. Her marginal cost is given by the equation MC = 200Q. a. In this market, what is Faye’s marginal revenue function? b. If Faye enters the market, how many website clients will she have, and what will her profit be? You can assume no fixed cost. Now imagine Faye asks you for advice. She knows you have just taken this course, and you learned about market power. c. Explain two ways Faye can achieve greater market power in this market. Faye takes your advice, and she is now the monopolist in a new market, where the demand curve is given by Q = 300,000 – 1,000P d. What is Faye’s new marginal revenue curve? e. In this new market, how clients will she have, and at what price will she sell her services? Now imagine you see all the profits Faye is making and you decide…
- 1. Which statement must be false?a) A firm with constant returns to scale in production will not have fixed costs.b) When a firm has increasing returns to scale, the upward sloping marginal cost curve lies above the average cost curve.c) All firms face diminishing returns to scale when they have a high output.d) When a firm produces the output which minimises average cost, marginal cost and average cost will be equal. 2. Which of the following statements about the relationship between marginal revenue, price, and the price elasticity of demand, is true?a) A perfectly elastic demand curve will be vertical, showing that the firm sells a fixed output at all prices.b) The more inelastic the demand curve, the flatter it will be where it meets the price (vertical) axis.c) If the price elasticity of demand PED = -1 at all points on a demand curve, then the firm can choose any level of output, and earn the same revenue.d) When a monopoly maximises its profits, demand for its output will be…Suppose that a perfectly competitive firm faces a market price of $7 per unit, and at this price the upward-sloping portion of the firm's marginal cost curve crosses its marginal revenue curveat an outpuut level of 1,400 units. If the firsm produces 1,400 units, it's average variable costs equal $6.50 per unit, and its average fixed costs equal $0.80 per unit. What is the firm's maximizing (or loss-minimizing output level? What is the amount of it's economic profits (or losses) at this output level?Suppose that the total revenue function of a firm is defined as TR= (P)(Q) where TR= f(Q). The usual notation applies. 1. Given its total revenue function, solve for the maximum revenue that the firm can earn. How many units of output should the firm sell to earn that amount of revenue? Note: Solve the problem using simple algebra only. Do not differentiate. 2. What are the roots of the total revenue function? Interpret economically.
- 2) Cost functionsConsider the following total cost function for an individual firm: C(q)= 10 +q + ¼ q^2 a- At what level of output is average cost at its lowest?b- Draw a graph showing firm average cost against quantity.c- Suppose that there is an industry with two identical firms, with this cost function. What is the industry total cost curve? What is the industry marginal cost curve?d- Suppose these two firms together act in a perfectly competitive manner. What is the price level in the case where these firms act perfectly competitively? What are the profits of the firms given perfectly competitive pricing?A small firm operating in a purely competitive market has fixed costs of $45 per day compensates each employee $96 per day and has daily input and raw material costs as indicated in the table below. A. What would be the profit maximizing level of production if demand increased such that each unit sold for $130?, will the company make an economic profit producing this quantity of output? b: suppose the demand significantly decreased so that price for a unit of ouput sold to $115 each. What should the firm do? Why?1- Suppose that the total cost function of a firm is given as follows;TC = 500 + 2Q2And the price of the firm’s product is determined by the market equilibrium at $100.a- Set the profit maximizing condition . Find the profit maximizing output level for this firm .b- What is the total revenue ?c- What is the total cost ?d- What is the profit earned by the firm ?e- Illustrate your answer by using a well-labeled graph .f- Denote the break even price level with Pb on the same graph .g- Denote the shut down price level with Ps on the same graph.h- Show the firm’s supply curve on the same graph .i- Does the firm function in short-run or long-run ? Why ?