A manufacturer of a new patented product has found that she can sell 70 units a week direct to the customer if the price is $78. In error, the price was advertised as $138, and, as a result only 40 units were sold in a week. The manufacturer's fixed costs of production are $50 a week and variable costs of $18 per unit. You are required to: a. Show the equation of the demand function linking price(P) to quantity demand(X), assuming it to be a straight line, is P+2X=218 b. Find where the manufacturer breaks even c. Find the quantity that maximizes profit d. Recommend a unit price which would maximize profit e. Determine the maximum profit f. Find the equation of new demand function, assuming a sudden change in trading conditions resulting a 20% reduction in demand at all price levels

A manufacturer of a new patented product has found that she can sell 70 units a week direct to the customer if the price is $78. In error, the price was advertised as $138, and, as a result only 40 units were sold in a week. The manufacturer's fixed costs of production are $50 a week and variable costs of $18 per unit. You are required to: a. Show the equation of the demand function linking price(P) to quantity demand(X), assuming it to be a straight line, is P+2X=218 b. Find where the manufacturer breaks even c. Find the quantity that maximizes profit d. Recommend a unit price which would maximize profit e. Determine the maximum profit f. Find the equation of new demand function, assuming a sudden change in trading conditions resulting a 20% reduction in demand at all price levels

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.13P

See similar textbooks

Similar questions

A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result, only 40 units were sold in a week. The manufacturers fixed costs of production are $1,710 a week and variable costs are $9 per unit. You are required to: a. Show the equation of the demand function linking price (P) to quantity demanded (X) assuming it to be a straight line is P = 118-x
– A certain cleaning company cleans professional offices and believes its staff can clean up to 300 office units a week at a labor and supply cost of $58 per unit. Preliminary pricing surveys indicate that if that if the company charges $100 per unit, it will have clients for 300 units. For every $5 price increase it can expect a demand of 10 fewer units. Assume the demand, s, is a linear function of price p. Find an equation for demand as a function of price. Find the Revenue and Cost functions, both of which are dependent on price p. Write the Profit function. Using Desmos, graph the Revenue, Cost, and Profit functions on the same coordinate plane. Label the axes and the functions and use an appropriate scale. Find the break-even points graphically and confirm algebraically. Label the regions of profit and loss on the graph. Algebraically find the price that results in a maximum profit. Conclusion: A price of $_________ results in a quantity of _____________ units…
James mainly sells confectionery items, newspapers, magazines and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too. Suppose the total cost function for rolls and pies is, TC = 900 + 50Q, Q = Q1 + Q2 Where Q1 and Q2denote the quantities of rolls and pies respectfully. If P1 and P2 denote the corresponding prices, the inverse demand equations are. Q1 = 70 - P1 and 0.5Q2 = 100 - P2 a)If James decides to make a total of 48 rolls and pies per day and charges different prices as above (that is, P1 ≠ P2 ), how many of rolls and pies each should he make in order to maximize the profit of a particular day? Estimate and interpret the Lagrange Multiplier λ [note: assume second-order conditions are satisfied]. b)Using your knowledge of input-output tables, explain which components of the economy will be affected if all convenience stores, including James’, closed down for three months due to the COVID-19. What would…
The FIA Formula 1 World Championship to be held during the 2021 Mexico City Grand Prix has a total cost function equal to CT = Q33 + Q2 + 125Q and an inverse demand function of P = 200−2Q. Now suppose there is a new company managing this event, so the total cost function becomes CT = 4Q. This new company intends to sell at two different prices depending on the place that the spectators occupy at the Hermanos Rodríguez Autodrome. For the Red Zone Boxes. The estimated demand will be q1 = 32−12p1 and for the Green Zone Boxes It will be q2 = 42 − p2. The number of tickets sold for the Red Zone and Green Zone will be: 15; 84 23; 16 15; 19 33; 45
The marketing research department for a company that manufacturers and sells gaming systems established the following price-demand function p(x)=240-30x Where p(x) is the wholesale price in dollars at which x thousand gaming systems can be sold, Find the revenue function when x thousand units are demanded Find the value of x that will produce maximum revenue. What is maximum revenue to the nearest thousand dollars? What is the price per gaming system that produces the maximum revenue?
. The second-largest public utility in the nation is the sole provider of electricity in 32 counties of southern Florida. To meet the monthly demand for electricity in these counties, which is given by the inverse demand function P = 1,200 − 4Q, the utility company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2 (so Q = Q1 + Q2). The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q21and C2(Q2) = 6,000 + 3Q22, respectively. Determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profits.
Suppose the demand function for a product is given by the function: D ( q ) = − 0.02 q + 80 D ( q ) = - 0.02 q + 80 Use integration (or other appropriate methods) to find the following: (Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 4 , 000 q = 4 , 000 .) A) The total actual revenue for q = 3 , 350 q = 3 , 350 units: Answer 1: B) The total possible revenue (for all quantities and prices): Answer 2: C) The Consumer's surplus corresponding to q = 3 , 350 q = 3 , 350 units: Answer 3: D) The "Not Sold" value corresponding to q = 3 , 350 q = 3 , 350 units: Answer 4
Suppose the profit maximizing firm sells the same good in two individual markets that it is able to keep separate. Since the price elasticity of demand is different in each market, the firm recognizes that rather than charge all customers the same price, it can increase profits by charging different prices in each of the two markets. The demand equations for each market are shown below: Market 1 P=25-2Q Demand The firm's Total Cost Function is: TC=5Q a) What is the optimal output in Market 1? b) What price will be charged in Market 1? Market 2 P=15-Q c) what is the optimal output in market d) what price will be charged in market e) what is the firm's total profit f ) illustrate your answer
Suppose you had a Bresnahan type of econometric study of the mid-range hotel (accommodation) industry, and this results in the following estimated demand and cost equations; Demand: P = 95.67 – 1.64Q + 0.75Y1 + 0.42Y1Q + 0.65 Y2 where P is price, Q is quantity, Y1 is the price of a close substitute and Y2 is consumers’ income. Cost equation: P = 2.67 + 0.21Q – 0.36Y1Q + 0.16W where P is price, Q is quantity, Y1 is the price of a close substitute and W is the wage rate in the industry. Using this information, calculate the Lerner index for this industry. Does market power exist in the industry? Justify your answer
Until recently, hamburgers at the city sports arena cost $2.50 each. The food concessionaire sold an average of 1,375 hamburgers on game night. When the price was raised to $3.00, hamburger sales dropped off to an average of 1,250 per night. The concessionaire's fixed costs were $1,133.60 per night and the variable cost was $2.60 per hamburger. Answer the following questions (A) through (F). (A) Assume that the relationship between price p and demand x is linear. Express p as a function of x and find the domain of this function. p=nothing The domain of p is nothing. (Type a compound inequality.) (B) Find the revenue function in terms of x and state its domain. R(x)=nothing The domain of R(x) is nothing. (Type a compound inequality.) (C) Assume that the cost function is linear. Express the cost function in terms of x. C(x)=nothing (D) Graph the cost function and the revenue function in the same coordinate system. Choose the correct graph below. Find the…
1.The price p in dollars of a certain commodity and the quantity x sold obey the demand equation p= -1/5x + 200 where 0<=x <=1000. Suppose that the cost C in dollars of producing x units is C= the square root of x divided by 10 + 400. Assuming that all items produced are sold, find the cost of c as a function of the price p.
(i) If the demand function for a particular commodity is p=−0.09x+51 and the total cost function C(x)=1.32x2+11.7x+101.4,where x is the level of production. Find (a) The revenue R(x) and profit Π(x). (b) All values of x for which production of the commodity is profitable. (ii) The total cost of manufacturing x units during the daily production run at a factory,is C(x)= x2+ x+900 dollars. Usually,x(t)=25t units are manufactured during the first t hours of production. (a) Express the total manufacturing cost as a function of t. (b) How much will have been spent on production by the end of the third hour? (c) When will the total manufacturing cost reach $11,000?