A boutique chocolate manufacturer produces 2 types of chocolate, Dark chocolate, and Milk chocolatedaily with a total cost function: TC = 7D + D x M + 3Mwhere:D is the quantity of the Dark chocolate (in kgs) andM is the quantity of the Milk chocolate (in kgs).The prices that can be charged are determined by supply and demand forces and are influenced bythe quantities of each type of chocolate according to the following equations:PD = 20-D + 5M for the price (in dollars per kg) of the Dark chocolate andPM 23 + 3D - M for the price (in dollars per kg) of the Milk chocolate.The total revenue is given by the equation:TR = PD XD + PM × Mand the profit given by the equationProfit = TR-TCFirst, use a substitution of the price variables to express the profit in terms of D and M only.Using the method of Lagrange Multipliers find the maximum profit when total production (quantity)is restricted to 2023 kgs. Note D or M need not be whole numbers.Be sure to show that your solution is a maximum point.

Lagrangian optimization problem has a following setup : Objective function & Constraint…

A boutique chocolate manufacturer produces 2 types of chocolate, Dark chocolate, and Milk chocolate daily with a total cost function: TC = 7D+Dx M + 3M where: D is the quantity of the Dark chocolate (in kgs) and M is the quantity of the Milk chocolate (in kgs). The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type of chocolate according to the following equations: PD = 20-D + 5M PM 23 + 3D - M The total revenue is given by the equation: TR= PD XD+PM × M and the profit given by the equation Profit = TR-TC First, use a substitution of the price variables to express the profit in terms of D and M only. for the price (in dollars per kg) of the Dark chocolate and for the price (in dollars per kg) of the Milk chocolate. Using the method of Lagrange Multipliers find the maximum profit when total production (quantity) is restricted to 2023 kgs. Note D or M need not be whole numbers. Be sure to show that your solution is a maximum point.

A boutique chocolate manufacturer produces 2 types of chocolate, Dark chocolate, and Milk chocolate daily with a total cost function: TC = 7D+Dx M + 3M where: D is the quantity of the Dark chocolate (in kgs) and M is the quantity of the Milk chocolate (in kgs). The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type of chocolate according to the following equations: PD = 20-D + 5M PM 23 + 3D - M The total revenue is given by the equation: TR= PD XD+PM × M and the profit given by the equation Profit = TR-TC First, use a substitution of the price variables to express the profit in terms of D and M only. for the price (in dollars per kg) of the Dark chocolate and for the price (in dollars per kg) of the Milk chocolate. Using the method of Lagrange Multipliers find the maximum profit when total production (quantity) is restricted to 2023 kgs. Note D or M need not be whole numbers. Be sure to show that your solution is a maximum point.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter12: The Partial Equilibrium Competitive Model

Section: Chapter Questions

Problem 12.9P

See similar textbooks

Similar questions

For many decades, the Royal Mail had a legal monopoly in the U.K. Companies in thepostal business have increasing returns to scale, then constant returns to scale, andthen decreasing returns to scale. The Royal Mail’s minimum average cost is £2 at 100million deliveries and its minimum marginal cost is £1 at 75 million deliveries.The demand for postage is zero at a price of £10, and demand is 300 milliondeliveries at a price of £0. Marginal revenue is zero at a price of £10 and 150 at aprice of £0.Note: Unless otherwise stated, the numerical answers in this question do not need tobe exact but should correspond to how you have drawn your graph. (a) Draw a large graph showing the Royal Mail’s average cost curve and itsmarginal cost curve. Show how many deliveries would be made, and at whatprice, if Royal Mail operated as a monopoly. Show the Royal Mail’s profit orloss on the graph.
For many decades, the Royal Mail had a legal monopoly in the U.K. Companies in thepostal business have increasing returns to scale, then constant returns to scale, andthen decreasing returns to scale. The Royal Mail’s minimum average cost is £2 at 100million deliveries and its minimum marginal cost is £1 at 75 million deliveries.The demand for postage is zero at a price of £10, and demand is 300 milliondeliveries at a price of £0. Marginal revenue is zero at a price of £10 and 150 at aprice of £0.Note: Unless otherwise stated, the numerical answers in this question do not need tobe exact but should correspond to how you have drawn your graph. New technology changes delivery firms’ technology. Now, the minimumaverage cost is £2 at 1 million deliveries and a minimum marginal cost of £1at 0.75 million deliveries. The government removes all price restrictions andallows free entry. Describe the long-term outcome for this market, using twographs, one at the firm-level and one at the…
For many decades, the Royal Mail had a legal monopoly in the U.K. Companies in thepostal business have increasing returns to scale, then constant returns to scale, andthen decreasing returns to scale. The Royal Mail’s minimum average cost is £2 at 100million deliveries and its minimum marginal cost is £1 at 75 million deliveries.The demand for postage is zero at a price of £10, and demand is 300 milliondeliveries at a price of £0. Marginal revenue is zero at a price of £10 and 150 at aprice of £0.Note: Unless otherwise stated, the numerical answers in this question do not need tobe exact but should correspond to how you have drawn your graph. The government makes a law restricting the price of postage to £1. Show theeffect of this policy in the short-run in a new, large graph. The graph shouldshow the firm’s average cost, marginal cost, marginal revenue, and consumerdemand. How much postage is bought? Show on your graph if the Royal Mailis in profit or loss, and by how much.
|1.6.1 A company manufactures and sells x dellphones per week. The weekly price-demand and cost equations are given below. p= 400 - 0.5x and C(x) = 20,000 + 140x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly revenue is $ (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly profit is $ (Round to the nearest cent as needed.)
A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…
The following graph plots the marginal cost (MC) curve, average total cost (ATC) curve, and average variable cost (AVC) curve for a firm operating in the competitive market for sun lamps. COSTS (Della) 72 04 8 56 24 16 . 0 Price (Dollars per lamp) MOD 8 12 36 48 60 10 ATC AVC 40 00 QUANTITY (Thousands of lamps) For every price level given in the following table, use the graph to determine the profit-maximizing quantity of lamps for the firm. Further, select whether the firm will choose to produce, shut down, or be indifferent between the two in the short run. (Assume that when price exactly equals average variable cost, the firm is indifferent between producing zero lamps and the profit-maximizing quantity of lamps.) Lastly, determine whether the firm will earn a profit, incur a loss, or break even at each price. Quantity (Lamps) ? Produce or Shut Down? Profit or Loss?
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Buddies Production Costs Quantity MC ATC of Ear Buds ($) ($) 20 1.00 25 2.00 1.20 30 2.46 1.41 35 3.51 1.71 40 4.11 2.01 45 5.43 2.39 50 5.99 2.75 55 8.47 3.27
11:30 l 4G I Homework 4 (section 2.1-2 & 2.2).pdf Economic Mathematics (1) Name ID Section 2.2 Revenue, cost and profit 1. If the demand function of a good is given by P-80 – 3Q, the fixed costs are 100 and variable cost are 5 per unit. Work out the profit when Q-10. 2. Find an expression for the profit function given the demand function 20+P= 25 and the 32 +5. Find the value of 0 for which the firm average cost function AC = (a) breaks even (b) makes a loss of 432 units (c) maximises profit. 2/2 !!
A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit function
Farmer Jones grows apples. The average total cost and marginal cost of growing apples for an individual farmer are illustrated in the graph to the right Assume the market for apples is perfectly competitive 40- According to the graph, farmer Jones will eam profit (positive economic profit as opposed to losses) at any market price above $ 10 per box. (Enter a numeric response using an integer) Assume that the market price specifically is $24 per box Iffarmer Jones produces the profit maximizing quantity, what will be her profit? S 36- To more easily identify the price and quantity, click on the graph to the nght, and then adjust the slider to change the price and quantity Each increment will increase the prce by $2. 32- MC 28- 24- 20- 16- ATC 12- 8- 4- :46 10 20 30 40 50 60 70 80 90 100 Quantity of Apples (boxes per month) Price and cost (dollars per box)
A company manufacturing laundry sinks has fixed costs of $100 per day but has totalcosts of $2,500 per day when producing 15 sinks. The company has a daily demand functionof q = 360 − p, where q is the number if laundry sinks demanded and p is te price ofa laundry sink. ) If production increases continuously, what is likely to be the average cost per sink? How many laundry sinks will the company need to produce in order to maximise it′s profits? What is the maximum profit?
Suppose that each firm in a competitive industry has the following as the Total cost: TC=50+ ½q2 Where q is an individual firm’s quantity produced. The market demand curve for this product is Demand: Q = 120 – P Where P is the price and Q is the total quantity of the good. Currently, there are 9 firms in the market What is each firm’s fixed cost? What is its variable cost? At what quantity efficiency of scale would be achieved? Give the equation for each firm’s supply curve Give the equation for the market supply curve for the short run What is the equilibrium price and quantity for this market in the short run? In this equilibrium, how much does each firm produce? Is there incentive for firms to enter or exit? In the long run with free entry and exit, what is the equilibrium price and quantity in this market? In the long-run equilibrium, how many firms are in the market?