(d) Find the royalty in each period. Show that, the discounted value of the royalty in each period is the same and it is equal to the shadow price of oil (λ). (e) Verify the Hotelling rule (i.e., show that the growth rate of the royalty is equal to the discount rate). (f) Provide an intuitive account of the Hotelling rule.
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(d) Find the royalty in each period. Show that, the discounted value of the royalty
in each period is the same and it is equal to the shadow price of oil (λ).
(e) Verify the Hotelling rule (i.e., show that the growth rate of the
royalty is equal to the discount rate).
(f) Provide an intuitive account of the Hotelling rule.
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- The price p (in dollars) and the quantity q sold of a certain product obey the demandequationq − 800 - 20P and 0 < p < 40 (answer iv and v) (i) Express the revenue R as a function of q.(ii) What is the revenue if 20 units are sold?(iii) What quantity q maximizes revenue? What is the maximum revenue?(iv) What price should the company charge to maximize revenue?(v) What price should the company charge to earn at least $3500 in revenue?True/False Average revenue is the derivative of total revenueIn 2012–2015, the price of jet and diesel fuel used by air freight companies decreaseddramatically. As the CEO of FedEx, you have been presented with the following proposals to deal with the situation:a. Reduce shipping rates to reflect the expense reduction.b. Increase the number of deliveries offered per day in some markets.c. Make long-term contracts to buy jet fuel and diesel at a fixed price for the nexttwo years and set shipping rates to a level that will cover these costs.Evaluate these alternatives in the context of the decision-making model presented inthe text.
- A company estimates that the relationship between. unit price and demand per month for a potential new product is approximated by p= $100.00-$0.10D. The company can produce the product by increasing fixed costs $17,500 per month, and the estimated variable cost is $40.00 per unit. What is the demand that maximizes revenue and the maximum revenue? What is the optimal demand, D*, and based on this demand, should the company produce the new product? Why? (Work out the complete solution by differential calculus, starting with the formula for profit or loss per month.)A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p= 75 -0.10 (D is the demand or quantity sold per month and p is the price in doilars). The fbxed cost is $1.000 per month and the variable cost is $30 per unit produced. a. What is the maximum profit per month for this product? b. What is the range of profitable demand during a month? a. The maximum profit per month for this product is S (Round to the nearest dollar.) b. The range of profitable demand during a month is from units to units. (Round up the lower limit and down the upper limit to the nearest whole number.)A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p=85-0.2D (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $1,500 per month and the variable cost is $20 per unit produced. a. What is the maximum profit per month for this product? b. What is the range of profitable demand during a month?
- A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p=70 -0.2D (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $700 per month and the variable cost is $40 per unit produced. a. What is the maximum profit per month for this product? b. What is the range of profitable demand during a month? a. The maximum profit per month for this product is $ (Round to the nearest dollar.)Demand for an item is constant at 40 units a week, and the economic order quantity is calculated to be 100 units. What is the reorder level if lead time is constant at 4 weeks? What is the effect of adding some margin of safety and raising the reorder level by ten units? What happens if the lead time (a) falls to 2 weeks or (b) rises to 6 weeks?Place the black point (plus symbol) on the graph to indicate the profit-maximizing price and quantity for BYOB. If BYOB is making a profit, use the green rectangle (triangle symbols) to shade in the area representing its profit. On the other hand, if BYOB is suffering a loss, use the purple rectangle (diamond symbols) to shade in the area representing its loss. Note: Dashed drop lines will automatically extend to both axes. Select and drag the rectangles from the palette to the graph. To resize, select one of the points on the rectangle and move to the desired position. PRICE (Dollars per can) 4.00 3.50 3.00 2.50 2.00. A 1.50 1.00 0.50 0 MC 05 ·D-D AC MR 1.0 1.5 QUANTITY TH 2.0 25 D 30 3.5 40 Monopoly Outcome Profit Loss ? 30 tv N MacBook Pro Ⓒ
- Netflix is increasing its streaming service from $9.99 per month to $10.99 per month. Which is must be true? a) They will lose less than 5% of subscribers b) They will not lose any subs c) They will lose no more than 20% of their subs d) They will lose less than 10% of their subsPixie Arts and Graphics, a medium scale printing press business has determined the equation that describes the relationship of the price and demand of one of its products as Price=150 - 0.01•D (D as Demand per unit) for an annual printing of this product. The fixed costs annually = P50,000 and the variable cost = P40 per unit. Requirement: a. What is the maximum profit that can be earned? b. What is the unit price at this point of optimal demand if demand is not to be anticipated to exceed more than 6,000 units annually? Hint: Profit (loss) = total revenue – total costs = (aD – bD²) – (Cf + CyD)Acme Drug Co. has a patent on the drug A-rene, the annual demand for which can be described by the demand curve: Q = 4500 - 300P. Production of the drug requires an annual fixed cost of $3,000 and a per unit marginal cost of $5. (i) How many units of the drug will Acme produce each year, and what price will it charge, in order to maximize its profits? What will be its annual profits? (ii) Now suppose that the Better Drug Co. has discovered B-rene, a new drug which seems to be identical to A-rene in all its effects. If Better enters the market, competition with Acme will conform to a Cournot duopoly. Better’s costs are identical to those of Acme. What would be the equilibrium outcome of this duopoly? Specifically, how much would each firm produce and what would be the price? How much profit would each firm make? Would Better find it profitable to enter the market? (iii) Would it be in the interests of society as a whole for Better Drug to enter into production? Identify the gainers and…