(b) You are given the following demand and supply functions le = a – ßp + o Q. = -y + ốp (α, β, σ, δ> i. Assuming that the rate of change of price overtime is directly proportional to the excess demand find the time path p(t) general solution and definite solution ii. What is the intertemporal equilibrium price iii. What is the market clearing equilibrium price iv. State the role of the complementary function and particular integral in relation to the equilibrium.
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- You are hired as a consultant at a revenue management firm and one of ourrecent clients wished to determine the optimum price for their consumer electronics product.The cost of the product is $100 and before retaining us, they had been selling the product at$200 because it felt like a nice round number. The current sales volume is 1000 units peryear. We examined the market preferences and buying behavior, and concluded that thiscompany’s marketplace has a price elasticity of 1 (i.e. Assume that an x% change in pricewill result in an x% change in sales volume for any x). What is the optimal price thatmaximizes total profit for this company? What are the sales volume, total revenue and totalprofit at the optimal price?Apply the properties of functions to correctly determine and interpret the break-even point in the following situations, using valid mathematical procedures and correct mathematical notation. Express your answer in terms of the context of the problem. The supply and demand equations for a certain product are: (1) and (2) respectively, where p represents the price per unit in dollars and q, the number of units sold per period. 3q - 200p + 1800 = 0 3q + 100p - 1800 = 0 Algebraically find the equilibrium price. Find and interpret the equilibrium price when a supplier tax of 27 cents per unit is imposed.Consider the “Trip Logistic” example discussed in class (i.e. base case). Please solve the same problem with each of the following changes, and compare the results with those of the basecase: a) The spot market price (in period 0) is reduced to $0.55 per sq. ft. per year. Assume that everything else remains the same as the base-case. b) There is a lower demand uncertainty: Demand can go up by 5% with p= 0.5 or down by 5% with 1 − p= 0.5. Assume that everything else remains the same as the base-case.
- an entrepreneur is setting up a storage facility which will provide storage bothat peak times and off peak times.The entrepreneur need to decide how much money storage Q1 t to supply at peak times, and how much storage Q2 to supply off peakit also needs to decide how to set up capacity K, where capacity is such that both K is equal or plus Q1 and K is equal or plus Q2The peak period demand fan storage is given by PI=7200 -Q1 and the off peak is give by P2=5400 -Q2 where P1 and P2 are the prices for units of storage at peak times and off peak respectively.the variable cost is 200 per unit of storage supplied and capacity costs are 100 per unit. Hence profits fpr the entrepreneurs are given by:(7200-Q1) Q1+ (5400-Q2) Q2 - 200 (Q1+Q2)-100 K where Q1 is less or equal K and Q2 is less or equal Ka) write down the Kuhn-Tucken conditions for this proble. b) Find the optimal outputs and capacity for this problemc) now suppose there is a substancial increqse in capacity costs, which rise to 2000…Let the production function be Q = 4∗K1/4L1/4 assume that both factors are variable. (a) Derive the contingent demand functions for K and L (b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function. (c) FindtheamountofKandLnecessarytoproduceQ=8whenv=16andw=1 (with minimal possible cost). (d) Find the average and marginal cost functions.The Almost-Graduating Senior Problem. Consider this situationfaced by a first-semester senior in civil engineering who is exhaustedfrom extensive job interviewing and penniless from excessivepartying. Mary’s impulse is to accept immediately a highly attractivejob offer to work in her brother ’s successful manufacturing company.She would then be able to relax for a year or two, save some money,and then return to college to complete her senior year and graduate.Mary is cautious about this impulsive desire, because it may lead tono college degree at al a. Develop at least two formulations for Mary’s problem.b. Identify feasible solutions for each problem formulation in Part (a).Be creative!
- My instinct is to treat this like a perfect complement scenario however I am unsure how to graph the LRXP. Could I have a walkthrough or explanation of how to derive the solution for this problem?The case of a tax over shifting (i.e., that the price after tax increases by more than the tax) A) is only possible in the case of perfect competition and a perfectly elastic demand curve. B) is only possible in the case of perfect competition and an inelastic demand curve. C) is only possible in the case of perfect competition and a vertical demand curve. D) is impossible with perfect competition, irrelevant of the elasticities In a two-period life cycle model, the intertemporal budget constraint has a kink if A) interest payments cannot be deducted but interest receipts are taxable. B) interest payments can be deducted but interest receipts are not taxable. C) all of the above. D) none of the above.A company produces and sells a consumer product and thus far has been able to control the volume of the product by varying the selling price. The company is seeking to maximize its net profit. It has been concluded that the relationship between price and demand, per month, is approximately D = 500 – 5p, where p is the price per unit in dollars. The fixed cost is $1,000 per month, and the variable cost is $20 per unit. Obtain the answer mathematically to the following questions: a.What is the optimal number of units that should be produced and sold per month? b.What is the maximum profit per month? c.What are the breakeven sales quantities and the range of profitable demand volume?
- Question Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Now consider two cases (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits? c. Analyze, with graphs, the two alternative pricing strategies…Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Required. Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market.? 2. Now consider two cases: (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging thesameprice in the two markets what are the profit…Wonopoly and natural resource prices Suppose that a firm is the sole owner of a stock of a natural resource. a. How should the analysis of the maximization of the discounted profits from selling this resource (Equation 17.63 be modified to take this fact into account? b. Suppose that the demand for the resource in question had a constant elasticity form q(t)=a[p(t)]b . How would this change the price dynamics shown in Equation 17.67? c. How would the answer to Problem 17.7 be changed if the entire crude oil supply were owned by a single firm?