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- 1. The cost function for a commodity is given by C(x) - 200+12x+0.1x² (S) and the demand funct is p-300-0.02x ($/unit) where x- quantity (demanded and produced). (a) What is the profit function for this commodity? (b) Find the marginal profit function. (c) What is the marginal profit when x-10?! (d) What does this marginal profit tell you? (e) Find the level of demand at which profit is a maximum. Show how you do this using calculus. (1) What is the maximum profit, and what is the selling price that realizes this profit? Ans: R(x)-300x-0.02x², P(x)=-0.12x² +288x-200, P'(10) - 285.6 (S), approximate increase in profit from selling one more unit when sales are at 10 units, solving P'(x)-0 gives max at unit. x-1200 units, max profit - $172,600, price = 300-0.02(1200)-$276 perYou're company manufactures on large scale unit and it has been shown that marginal or variable cost are given by this function (92-2x)sh where xis the number of units of output per annum the fixed costs are 800000 annually, it has also been shown that the marginal revenue which is the gradient ot the total revenue is given by (112-2x) ... required determine by integration the total cost, the total revenue , the break even point of your company and the number of units of output that would maximise total revenueCOURSE: MICROECONOMICS - TAX REGULATIONS The local diesel market is represented by Q = (912 - P)/12.5 and Q = (P - 315)/11where P is in dollars (USD) per liter of fuel and Q shows liters of fuel (in millions). Currently a tax of USD 130 per liter of diesel is charged.It is requested:(a) Calculate the amount (Q) that is transacted after the tax has been applied. Already solve few hours agob) Show in detail the calculations of a). Is there any difference between the price observed by suppliers and demanders? If so, what is the price observed by the producer and what is the price observed by the consumer? how much is the government's revenue? If there is an efficiency loss, how much is it? Already solve few hours agoc) At present, there are arguments in favor of increasing the tax on diesel and others in favor of decreasing it (at least temporarily). Mention at least ONE argument in favor of increasing this tax and ANOTHER argument in favor of decreasing it. And finally, conclude in…
- COURSE: MICROECONOMICS - TAX REGULATIONS The local diesel market is represented by Q = (912 - P)/12.5 and Q = (P - 315)/11where P is in dollars (USD) per liter of fuel and Q shows liters of fuel (in millions). Currently a tax of USD 130 per liter of diesel is charged.It is requested:(a) Calculate the amount (Q) that is transacted after the tax has been applied.b) Show in detail the calculations of a). Is there any difference between the price observed by suppliers and demanders? If so, what is the price observed by the producer and what is the price observed by the consumer? how much is the government's revenue? If there is an efficiency loss, how much is it? GRAPHc) At present, there are arguments in favor of increasing the tax on diesel and others in favor of decreasing it (at least temporarily). Mention at least ONE argument in favor of increasing this tax and ANOTHER argument in favor of decreasing it. And finally, conclude in favor of which argument you are in favor of.SuProse a liim hus revenue R=15t- 5q2 und (Ost (= 93-13.5e+ 50+ 40. Make a sketch of average Variable cOst, marginal (ost and maigina fevenue.The demand for q units of a product depends on the price p (in dollars) according to 512 P q= - 1, for p > 0. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when the price is as follows. (a) $16 (b) $64 Interpret the instantaneous rate of change. O If price decreases by the absolute value of this amount, the demand will drop by 1 unit. O If price increases by $1, the demand will increase by the absolute value of this number of units. If price decreases by $1, the demand will drop by the absolute value of this number of units. If price increases by the absolute value of this amount, the demand will drop by 1 unit. If price increases by $1, the demand will drop by the absolute value of this number of units. Interpret the instantaneous rate of change. O If price decreases by the absolute value of this amount, the demand will drop by 1 unit. O If price increases by $1, the demand will increase by the absolute value of this number of units.…
- 920 it bait of 289301 Sindspis ON SEU pilkupeni A30S AO +32 monulo2 An economist for a sporting goods company estimates the revenue and Cost functions for the production of a new snowboard. These Functions are R(x) = -x ² +10x and ((x) = 4x+5, respectively, where x is the number of Snowboard's produced in thousands. The average profit is defined by the function AP(x) = P(x), where pox) is the profit function & Determine the production levels that make AP(x) > 0 P-xd)A two Product finm faces the follow- = 40-2P1 demand and Cost function 8- a) Find the output levels that satiaty the 12 demand amd 40-2P,-P2 タ,=35-P、- 8 follow- ng Cont function8 32 Demand function. C%=8it 20+ 10 cost function. a) Find the output levels that sati. order Conditions ythe tor maximum profit. 6)check the 2nd (ondition. Can you conclude that this Problem Posses a Order for sufficient unique maximum) c)What in the maximal profit?The Rainwater Brewery produces beer. The annual fixed cost is $150,000, and the variable cost perbarrel is $16. Price is related to demand according to the following linear equation.v -75,000 1,153.8pDevelop the nonlinear profit function for the brewery and determine the price that will max-imize profit, the optimal volume, and the maximum profit per year.
- Given the demand functions, (iii) P = 45 (a) Write down the equations for TR. (b) Calculate the number of units which must be sold to maximize TR. Calculate the maximum TR. (c) State the values of Q at which MR and AR are zero.Problem 6Cannes Croissants (not a real company) wishes to determine the optimum production quantity for its topselling product, almond croissants. The annual demandfor almond croissants is 12,000 units. The setup costs fora production run of the croissants is US$15. The holdingcost per unit per year is US$0.50. Production is mostefficient when 80 croissants are produced per day. Thecompany operates 300 days during a year.a What is the economic production quantity (EPQ)?b How many production runs will there by per year?c What is the maximum inventory level?d What is the total annual cost (in US dollars)?e What is the length of a production run in days?(a) What is the profit-maximizing level of output and how much daily profit will the producer below earn if the price of pizza is $ 2.50 per slice? MC S/slice ATC AVC 2.50 1.40 slices/day 570