A small town has two bakeries, Acme and Fat Apple. Acme's marginal cost to make a loaf of bread is $1 and Fat Apple's marginal cost is $2. Acme's demand function is given as Q₁ = 14 - P₁ -0.5P₂ and Fat Apple's demand function is Q₂ = 19 -0.5P₁ - P2 where P₁ (P₂) is Acme (Fat Apple)'s price in dollars per loaf of break and Q₁ (Q₂) is measured in thousand loaves of Amce (Fat Apple)'s bread (respectively). What is Acme's profit function? O O - P₂² +15P2-0.5P1 P2 +0.5P₁ - 14. -P₁²+15P₁ -0.5P₁P2 +0.5P2 - 14. -P₁²+10P1 -0.5P₁ P2+ 0.5P2 O + P₁²-15P₁ +0.5P1 P2 -0.5P2 + 14.
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- A small town has two bakeries, Acme and Fat Apple. Acme's marginal cost to make loaf of bread is $1 and Fat Apple's marginal cost is $2. Acme's demand function is given as Q₁ = 14 - P₁ - 0.5P2 and Fat Apple's demand function is Q2 = 19 -0.5P1 - P2 where P₁ (P2) is Acme (Fat Apple)'s price in dollars per loaf of break and Q₁ (Q2) is measured in thousand loaves of Amce (Fat Apple)'s bread (respectively). Find Nash equilibrium prices. O O O P1 = 10.2 and P2 = 9.2. P1 = 5.2 and P2 = 9.2. P1 = 4.4 and P2 = 8.2. P1 = 5.5 and P2 = 9.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 £ Numberthe 9. You own a bakery and the inverse demand function for your cakes is P = 8 – 1.5Q. If cost of producing cake is C = 0.5Q, determine the profit-maximizing quantity, and the profit-maximizing price.
- 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 flour mill buys its wheat from two different farms, then processes the wheat into flour. Wheat from Farm X costs the mill $7 per bushel, and wheat from Farm Y costs the mill $15 per bushel. The selling price (in dollars per bushel) for the mill's wheat can be modeled by p(x, y) = 500 x y where x is the demand for the flour milled from Farm X's wheat and y is the demand for flour milled from Farm Y's wheat. Assume that x and y may be zero (so the mill only buys from one of the suppliers) and that the mill can by 1/2 of a bushel. Then the maximum profit is attained when x = y = bushels bushels The amount of the flour mill's maximum profit is $Q.5 A firm is making two products A & B. Each unit of A incurs a cost of production to the tune of $150 and that of B incurs a cost of $200. Product A earns a profit of $15/unit and B gets $20/unit. The estimated monthly demand of both A & B is at maximum 500 units. Monthly production budget is set at $50,000.How many units of A & B should the firm make in order to maximize profit. Conduct sensitivity analysis and answer the following questions: 1. State the optimal solution. 2. What is the objective function value? 3. Find out the range of profit for A in the objective function for which the above solution remains optimal. 4. Which constraint/s is/are binding? 5. Interpret the shadow price for production budget.
- Diego's Pizza is the sole supplier of pizzas in a little town. The market demand for pizzas is estimated by: Q = 600 – 100P The production function for Diego's Pizza is Q 135L, where L is the number of workers. He pays a wage of 81, and his fixed costs are 600. a) What is the optimal number of workers at Diego's Pizza? b) Find the price, output, and profit at the optimal number of workers. c) Find the elasticity of demand at the price set by Diego's Pizza. d) Calculate the Lerner Index for Diego's Pizza. Page 2 af 3Assume demand is: P = 76 – Q - and total cost is: TC = 20 + Q² What is the quantity that maximizes profit? (type your answer below)Jesaki Inc. is trying to enter the widget market. The research department established the following price-demand, cost, and revenue functions: p(x) = 60 - 1.20x C(x) = 210 + 12x R(x) = xp(x) = x(60 - 1.20x) Revenue function Price-demand function Cost function where x is in thousands of widgets and C(x) and R(x) are in thousands of dollars. The price p(x) is the price in dollars of one widget when the demand is a thousand widgets. All three functions have domain 1 ≤ x ≤ 50. Use this information to answer questions 1-10 below.
- you are an accountant for a manufacterer of radios. the demand function for the tablets is p= 40-4x2 where x is the number of tablets produced in millions. it costs the company $15 to make a tablet. write an equation for the manufactures profit as a function of the number of tablets produced. the company currently produces 1 million tablets and makes a profit of $21000000, but you would like to scale up production a bit, what greater number of tablets could the company produce to yield the same profitGeorge has been selling 5,000 T-shirts per month for $8.50. When he increased the price to $9.50, he sold only 4,000 T-shirts. Which of the following best approximates the price elasticity of demand? -2 -2.2 -2.6 -1.8 Suppose George's marginal cost is $5 per shirt. Before the price change, George's initial price markup over marginal cost was approximately . George's desired markup is . Since George's initial markup, or actual margin, was than his desired margin, raising the price was .You own a bakery and the inverse demand function for your cakes is P=8-1.5Q. If the cost of producing cake is C=0.5Q, determine the profit-maximizing quantity, and the profit-maximizing price.