As an owner of a small business, you want to determine the optimal monthly advertising expenditures for the business. Your total monthly cost is TC = 4Q+ 0.0005Q² + A where A is the advertising expenditure. Your marginal revenue from advertising is constant at MRA = $4, and the advertising elasticity of demand is 0.4. Suppose you know the profit maximizing level of output is Q = 12,000 per month. Find the optimal level of advertising expenditure? Use a graph to demonstrate your answer.
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- Suppose demand and supply curves for you company’s product are given by:QD = 10 -XP QS =5 +YP You will need to find value for X between [0.1 -3] and Y between [0.1 -3] based on the elasticity of demand and supply. This elasticity in turn depends on the type of product, marketstructure and competitive advantage of the company. In this case, the product is an electric car and the price elasticity of demand is high.At an amusement park with a “horror” roller coaster, management has estimated that the average visitor has a demand function P = 9 – (Q/3), where P is the average ride price and Q is the number ofof routes per visitor. The total cost to the average visitor is C = 1 + Q.Management is considering two pricing schemes. Either charge P per ride, or charge a general admission price that will allow the visitor to do as many rides as they want.(a) If management chooses per-ride pricing, what price will it charge and what will be the profit per visitor?(b) If he chooses a general entry price this will be such as to extract all of the surplus from each consumer. What will be the general admission price and profit per visitor?(hint: the general input price will be revenue P×Q + CS, where CS = 0.5×(9 – Ρ)×Q is the consumer surplus corresponding to the profit-maximizing quantity).You own a private parking lot near shard building with a capacity of 600 cars. The demand for parking at this lot is estimated to be Q=1,000 - 2P, where Q is the number of customers with monthly parking passes and P is the monthly parking fee per car. Derive your marginal revenue schedule. What price generates the greatest revenues? Your fixed costs of operating the parking lot, such as the monthly lease paid to the landlord are £25,000 per month. In addition, your insurance company charges you £20 per car per month for liability coverage and the shard building charges you £30 per car per month as part of its policy to discourage the use of private cars in the city centre. What is your profit maximising price?
- Bluth’s Bananas is considering expanding its retail operations for its one-of-a-kind frozen banana stands on Jones Beach, which is 10 kilometers long. Bluth’s Bananas estimates that the typical day has 2,000 visitors to the beach, spread uniformly, and that each will demand a single frozen banana provided the price plus any disutility of traveling to a stand does not exceed $6. To visit a stand a beach goer incurs a disutility of $0.50 for each 1/4 kilometer they have to walk to reach a stand. Each Bluth Banana costs $0.75 to make and each stand requires an operating fee to be paid to the city of $50 per day. Determine the equilibrium number of stands Bluth’s Bananas should operate on the beach given it is not in competition with any other firm. Determine the profit maximizing price for the bananas and calculate the profit realized by BB in equilibrium.A firm with market power has an individual consumer demand of Q = 20 − 2P and total costs of C = 3Q. What is the optimal amount of this product to package in a single block?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?
- A manager of a nightclub realizes that demand for drinks is more elastic among students and is trying to determine the optimal pricing schedule. Specifically, he estimates the following average demand for his customer types: Under 25: qr =18-5p Over 25: q=10-2p The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the club $2 to make. If the manager can charge a separate entry fee and a price per drink for each group, what two-part price will the manager set for reach group. Now suppose that once again it is impossible to identify which group the customers belong. Suppose the manager lowers the price of drinks to equal to marginal cost and still wanted to attract both customers, what entry fee would the manager set? Compare the profits earned in parts a) to d). Which scheme would you choose if you could not identify customer type and which would you choose if you could identify customer type.You own a private parking lot near City University with a capacity of 600 cars. The demand for parking at this lot is estimated to be Q=1,000 - 2P, where Q is the number of customers with monthly parking passes and P is the monthly parking fee per car. Your fixed costs of operating the parking lot, such as the monthly lease paid to the landlord are £25,000 per month. In addition, your insurance company charges you £20 per car per month for liability coverage and the City of London charges you £30 per car per month as part of its policy to discourage the use of private cars in the city centre. What is your profit maximising price?If demand function is given as the following: Qz = 230 -2.75 Pz + 0.5 I + 1.2 Pm + 0.6A Where Qz is quantity of Good z sold, Pz is price of Good z per unit, I is per capita income, Pm is price of competitor and A is the amount of advertising spent. Current values: Pz= RM 55 I= RM 9000 Pm= RM 50 A =RM 12,000 a) Should the firm consider giving a price discount in order to increase total revenue?
- The Edgewater Hotel in Seattle has 210 guest rooms. When they charge a discounted rate of $250 per night, the occupancy rate is 80%. Experience has shown that each $10 increase in rate results in 5 fewer occupied rooms. Define the function that models the total revenue to the hotel as a function of x, the number of $10 price increases.A private golf club has two types of members. Serious golfers each have the demand curve Q = 250 - 10P, where Q represents the number of rounds played per year and P is the per- round price. Casual golfers have the demand curve Q = 100 - 10P. The club has 5 serious and 60 casual golfing members and faces a constant marginal cost and average cost of $ 5 per round played by either type of member. The club cannot distinguish high demanders from low demanders but is considering deploying a 2-part tariff pricing system? Specifically, the club is considering a per-unit price of $5 and a per-unit price of $6. What should they do and what are the profits they will earn? Be very clear in how you arrive at your answer.If your marketing department estimates that the semiannual demand for the highlander is q=150,000. - 1.5 P, what price should you charge in order to maximize revenues from the sales of highlander