QUESTION 2 (a) Imagine you have started a new business and the demand and cost equations are given as follows: P=120-0.5Q C=420+60Q+Q² Find your firm's optimal quantity, price and profit. [You may assume the firm is a profit maximizing firm] (i) (ii) Supposing the firm finds that it can actually sell as much as it wants of this product at a Price=120. Find the firms optimal output.
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- Q2)Tony Keonte owns a factory that manufactures Eye-Games. His weekly profit (in thousands of dollars) is given by the following function: P(x) = -4x2 + 80x- 300. Where x is the number of Eye-Games sold. a) What is the largest number of Eye-Games that the company can sell and still make profit? (25 points) b) How many Eye-Games will the firm have to produce and sell in order to maximize profit? (25 points)Student Resources Working at Clayton.... 3/3 practice Gigantic Pharmaceutical Corporation has a patent on a prescription drug, making it the only manufacturer of that prescription drug. Gigantic is currently earning a positive economic profit. (a) Draw a correctly labeled graph for Gigantic and show each of the following. (i) The profit-maximizing quantity, labeled QG (ii) The profit-maximizing price, labeled PG (iii) The average total cost curve, labeled ATC (iv) The area representing the consumer surplus, shaded completely (b) Suppose the demand for the prescription drug increases, and Gigantic hires its warehouse workers in a perfectly competitive labor market. (i) What will happen to Gigantic's demand for warehouse workers? Explain. (ii) What will happen to the wage rate Gigantic pays its warehouse workers and the number of warehouse workers it hires? (c) After Gigantic's patent expires, another firm enters the prescription drug market and produces an identical drug that sells for…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…
- Lukanga Water has been providing water services in the Central Province for more than 20 years. Business analysts estimated the demand for water is P 40- 5Q, where Q is the number of clients served (in thousands) and P is the price charged (in millions of Kwacha). Lukanga Water total costs are determined as TC = 10 - 0.75Q. (a) How much is the profit maximizing level of output? (b) How much is Price at profit maximizing level of output? (c) Calculate the Profit level."The Hickory Cabinet and Furniture Company makes chairs. The fixed cost per month of making chairs is $7,500, and the variable cost per chair is $40. Price is related to demand, according to the following linear equation: v = 400 - 1.2p Graphically illustrate the profit curve developed . Indicate the optimal price and the maximum profit per month.22) Ace Shoe Company sells heel replacement kits for men's shoes. It has fixed costs of $6 million and unit variable costs of $5 per pair. Suppose a consultant tells Ace it can sell 700,000 heel repair kits, what price must it charge to achieve a profit of $2.5 million? (Please show your calculation steps
- (b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40−4q2where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?Consider total cost and total revenue given in the following table: TABLE IN IMAGE Calculate profit for each quantity. How much should the firm produce to maximize profit?(ii) Calculate marginal revenue and marginal cost for each quantity. Graph them. (Hint: Put the points betweenwhole numbers. For example, the marginal cost between 2 and 3 should be graphed at 2½.) At what quantitydo these curves cross? How does this relate to your answer to part (a)?(iii) Can you tell whether this firm is in a competitive industry? If so, can you tell whether the industry is in along-run equilibrium? (8.75)(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Problem з
- 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 function7. Assume that the marginal cost curve is given by mc(q) = 100 + 2q. (a) If the price is $160, what is the optimal production for the firm? What if the price is $120? (ignore the shut-down decision for this part) (b) Assuming that the market is cleared at $160 (no shortage/surplus). If the market demand is equal to 10,000 units of the product. How many firms are currently operating (n) in the market? (Hint: if the market clears qª = n x q°) (c) If the total cost curve is TC 256 + 100g + q², what's the average total cost curve? %3| what's the break-even price? (d) If the demand curve is given by qd = 8, 452 – p, what's the long-run equilibrium price, the equilibrium quantity and the long-run total number of firms (n) in the industry?|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.)