You are a manager at Boston Brew'ns, the official microbrewery of the Boston Bruins. Applying what you learned at Cal State East Bay prior to moving to the east coast, you have estimated the cost function for brewing beer to be c(Q) = 2+Q+Q². Further, you have estimated the elasticity of demand for your signature beer, finding it to be =-1.5. Your firm has some price setting power because you and the other breweries in town offer differentiated products. The firm is currently charging a price of $6 per beer and selling 100 beers. Is this a profit-maximizing price? Explain. Should you increase or decrease the markup? Explain.
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- Q1: Analytical part - 8% Best Orange Juice Company is located in Oman. The cost function for total orange juice production (x) is given by C(q) = 0.25x2. Their orange juice is demanded only in Muscat (Muscat demand is Xm- 100-2Pm) and Salalah (Salalah demand is X 100-4Ps). Therefore, the total demand is x-xm+ Xs. If the company can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price would it charge in each location? Answer:Discuss the importance of price elasticity of demand, income elasticity of demand and cross price elasticity of demand to a sales manager selling soft drinks like Coca Cola If a firm faces the Marginal Cost schedule MC = 180 + 0.3Q2 and the MR schedule is MR = 540 = 0.6Q2 and that Total Fixed costs are $65. What is the maximum profit it can make? Assume that the second-order condition for maximum is metDalahla Company Limited, focusing on producing tooth paste (in units) has a demand function4? = 35 − 0.5?. If total fixed cost is GH¢80 and average variable cost per unit function is 3? −51+325/Q, where Q is number of tooth paste produced and P is the price per tooth paste (in GH¢).What is the total profit at the profit maximizing level of output, and what is the best pricing policyoption?
- Bavarian Crystal Works designs and produces crystal wine decanters for export to international markets. The marketing manager of Bavarian Crystal Works estimates the demand curve for each month to be: P=1,000-0.0025Q where Q is the number of wine decanters produced annually. Bavarian Crystal Works also pays a lease for its factory and equipment every month in the amount of $1,000,000. Finally, the cost to produce each wine decanter is $200. What is the marginal revenue at 40,000 units? If Bavarian Crystals is currently producing 40,000 units would you recommend they increase their production?The demand curve for Blivets has the formula P =h(q) = 12-4q Where q is measured in thousand of Blivets and p is measured in dollars. We Get Total revenue(measured in thousands of dollars) TR(q)=q*h(q). The total cost (measured in thousands of dollars ) of manufacturing Blivets Is given by the formula TC(q)= q+1. Due to the limited supply of raw material, we Cannot manufacture more than 3500 Blivets ( q=3.5) d) b) find the value of q in the interval between q=0 and q=3.5 thousand blivets at which TR(q) reaches its largest valueThe demand curve for Blivets has the formula P =h(q) = 12-4q Where q is measured in thousand of Blivets and p is measured in dollars. We Get Total revenue(measured in thousands of dollars) TR(q)=q*h(q). The total cost (measured in thousands of dollars ) of manufacturing Blivets Is given by the formula TC(q)= q+1. Due to the limited supply of raw material, we Cannot manufacture more than 3500 Blivets ( q=3.5) A) write the formula for TR(q) and TR'(q) ( simplify your answer as much as possible) b) find the value of q in the interval between q=0 and q=3.5 thousand blivets at which profit is greatest c) find the formula for Total profit p(q) of selling q thousand blivets d) b) find the value of q in the interval between q=0 and q=3.5 thousand blivets at which TR(q) reaches its largest value
- A boutique beer brewery produces 2 types of beers, Dark-ale and Light-ale daily with a total cost function given by TC = 8D + D XL+ 3L where D is the quantity of Dark-ale beer (in kegs) (not kg), and L is the quantity of Light-ale beer (in kegs) The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type according to the following equations: PD=53-D + L for the price $/keg for Dark-ale beer PL = 42 + 2D-L for the price $/keg for Light-ale beer The total revenue is given by the equation: TR = PD X D + P₁ x L And the profit given by the equation: Profit = TR - TC (a) Write down the profit in terms of D and L only. (b) The total production (quantity) of both beers combined is restricted to 191 kegs. Formulate the problem using the method of Lagrange multipliers. Find the maximum profit for the appropriate values of D and L. Note that they need not be whole numbers. Note that to get full marks, you need to check that the…The inverse demand for tea is given by P= 10 – 0.04Q, where Pis the price per a gram of tea and Qis the total number of grams of tea brought to market. There are two tea shops in the market. Shop 1's cost function is given by C = 0.01q,?, where qı is the number of grams of tea it brings to market. Shop 2's cost function is given by C2 = 0.01q2², where qp is the number of grams of tea it brings to market. Given that the two shops compete by setting output (Cournot), answer the following. a) Identify shop 1's reaction function to shop 2's output to within 2 decimal places (e.g. 0.33). 91= Number - Number 92 b) Identify shop 2's reaction function to shop 1's output to within 2 decimal places (e.g. 0.71). q2= Number Number 91 c) To within two decimal places (e.g. 0.63) what is the equilibrium output level of each shop and the equilibrium per gram price for tea. Shop 1 will produce Number grams of tea and shop 2 will produce Number grams of tea. The equilibrium market price is £ NumberA local microbrewery has total costs of production given by the equation TC=500+10q+5q^2. This implies that the firm's marginal cost is given by the equation MC=10+10q (you do not need to be able to show this). The market demand for beer is given by the equation QD=105 – (1/2)*P. a) Write the equations showing the brewery's average total cost .
- The inverse demand for tea is given by P = 8 – 0.03Q, where Pis the price per a gram of tea and Q is the total number of grams of tea brought to market. There are two tea shops in the market. Shop 1's cost function is given by C = 0.02q,?, where q, is the number of grams of tea it brings to market. Shop 2's cost function is given by C2 = 0.02q22, where q2 is the number of grams of tea it brings to %3D %3D market. Given that the two shops compete by setting output (Cournot), answer the following. a) Identify shop 1's reaction function to shop 2's output to within 2 decimal places (e.g. 0.33). 91= Number Number 92 b) Identify shop 2's reaction function to shop 1's output to within 2 decimal places (e.g. 0.71). q2= Number Number 91 c) To within two decimal places (e.g. 0.63) what is the equilibrium output level of each shop and the equilibrium per gram price for tea. Shop 1 will produce Number grams of tea and shop 2 will produce Number grams of tea. The equilibrium market price is £…A local microbrewery has total costs of production given by the equation TC=500+10q+5q^2. This implies that the firm's marginal cost is given by the equation MC=10+10q (you do not need to be able to show this). The market demand for beer is given by the equation QD=105 – (1/2)*P. a) What is the break even quantity in short run.Bavarian Crystal Works designs and produces crystal wine decanters for export to international markets. The marketing manager of Bavarian Crystal Works estimates the demand curve for each month to be: P=1,000-0.0025Q Where Q is the number of wine decanters produced monthly. Bavarian Crystal Works also pays a lease for its factory and equipment every month in the amount of $1,000,000. Finally, the cost to produce each wine decanter is $200. What quantity would maximize profits? What is the optimal price for Bavarian Crystals to charge?