(1) Von-Thünen Model I A coffee shop is located at M (where x=0) and charges marginal cost prices for its coffee (i.e., c-p). Customers walk to the coffee shop to buy coffee and, aside from the purchase price, incur travel cost of (tx²), measured from the shop. The shop's market reach is 2.3 km and t=2. If customers' WTP for the shop's coffee is $12.83 what is the product's price in equilibrium?
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- A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of plywood is $800,000 per month. The variable cost per thousand board feet is $155.50. The price charged will be determined by p=$600−(0.05)D per 1,000 board feet. a. For this situation, determine the optimal monthly sales volume for this product and calculate the profit (or loss) at the optimal volume. b. What is the domain of profitable demand during a month?An Accra Chemical Factory discharges waste products into a river. These wastes kill many tilapia that are swimming upstream to spawn. While there will no doubt be other ecological damages from the chemical effluent, we wish to focus on those of the fishery. Let E be the tonnes of chemical effluent discharged per month. The equation for Marginal Damages (MD) is MD = 6E. The firm’s Marginal Abatement Cost (MAC) is given by MAC = 800 – 10E. a. Sketch the MD and MAC functions graphically on the same axes. b. Suppose E0 is the point where MAC = 0. Find the total damages (TD) to fishery by the factory per month.An Accra Chemical Factory discharges waste products into a river. These wastes kill many tilapia that are swimming upstream to spawn. While there will no doubt be other ecological damages from the chemical effluent, we wish to focus on those of the fishery. Let E be the tonnes of chemical effluent discharged per month. The equation for Marginal Damages (MD) is MD = 6E. The firm’s Marginal Abatement Cost (MAC) is given by MAC = 800 – 10E. a. Suppose the government invokes a liability law that requires polluters to compensate those damaged in an amount equal to the damages caused. Will the factory change its emission levels in response to the liability laws? Explain. b. If E* is the socially efficient level of emission, prove that reducing effluent to E* is a better strategy for the chemical factory than not reducing waster discharged and staying at E0.
- A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 160 -0.02 × Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing) = $51,000 and the variable cost per unit = $35. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 4,000 units per year. The maximum profit that can be achieved is $144,313. (Round to the nearest dollar.) The unit price at the point of optimal demand is $ per unit. (Round to the nearest cent.)The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x)=26x +18,625 and R(x)-200x-0.2x² for 0≤x≤ 1000. (A) Find the value of x where the graph of R(x) has a horizontal tangent line (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0sxs 1000. Find the break-even points. Find the x-intercepts of the graph of P(x) (A) R(x) has a horizontal tangent line at x =A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150 − 0.01 × Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing) = $50,000 and the variable cost per unit = $40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 6,000 units per year.
- The cost of controlling carbon dioxide emissions [C(E)] at a firm goes up rapidly as the amount of emissions (E) increase. Let's assume the relationship is defined by the function below. C(E)= 5000+ 40E +2E² E20 where E is measured in tonnes per year and C is measured in dollars per year. a) Determine the Marginal Cost function for controlling carbon dioxide emissions and find the marginal cost at 50 tonnes of emissions: b) Determine the Average Cost Function for controlling carbon dioxide emissions and find the tonnes of emissions at minimum average cost. c) The government is charging a tax of $270 for every tonne of carbon dioxide emitted. At, 50 tonnes of emissions, is it profitable for the firm to control emissions on its own or pay the carbon tax?Leonard Presby, Inc., has an annual demand rate of 1,000units but can produce at an average production rate of 2,000 units. Setup cost is $10; carrying cost is $1. What is the optimalnumber of units to be produced each time?It is known that a certain company sells each kg of the product it manufactures at $80, it is also known that the total manufacturing cost "CT" is given by the function CT=(1/1000)x2 +100 , where "x" are the kg of product produced. a) How many units of "x" must the company sell to break even? Value = 100 points.b) How many units of "x" is the optimal quantity that should be sold to optimize the producer's profit? Value = 100 points.c) How many monetary units does that optimal profit for producers amount to? (remember, you will have to prove it mathematically either by the method of the first or by the method of the second derivative). Value = 100 points.
- (1) A company in Scotland bottles sparkling water. The fixed cost per month to produce bottled water is $35,000, and the variable cost is $0.2 per bottle. Price is related to demand according to the following equation: v = 4,000 – 1.1p Determine the optimal price using a nonlinear profit analysis. (2) A tailor on Savile Row is producing suits. The fixed cost per month producing suits is $13,000, and the variable cost is $140 per suit. Price is related to demand, according to the following equation. v = 600 – 1.5p Determine the optimal price using a nonlinear profit analysis.A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price=160−0.02×Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing)=$47,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 4,000 units per year. The maximum profit that can be achieved is $? (Round to the nearest dollar.) The unit price at the point of optimal demand is $? per unit. Your software company recently instituted a highly regarded training program for newly hired software developers. The benefits of this program include not only the benefits to employees, but also the goodwill generated by an increase in your reputation among customers and professional groups. The costs of this training program include all of the labor, space, and consultants necessary. Suppose these benefits and costs are givenby B(Q) = 100Q − 2Q2 and C(Q) = 10Q, where Q represents the amount of hours each software developer should spend in training. (Note that MB = 100 − 4Q, MC = 10, and also that time can be measured in fractions of one hour.) a. What level of Q maximizes the total benefits of your newly introduced training program?b. What level of Q minimizes the total costs of the program?c. What level of Q maximizes the net benefits?