Shortly find the mathematical expression of Lagrangian multiplier of “constrained revenue maximization”, “constrained output maximization” and “cost minimization subject to revenue constraint” then find the mathematical expression of: (a) relationship between Lagrangian multiplier of “constrained revenue maximization” and “constrained output maximization”
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Shortly find the mathematical expression of Lagrangian multiplier of “constrained revenue maximization”, “constrained output maximization” and “cost minimization subject to revenue constraint” then find the mathematical expression of:
(a) relationship between Lagrangian multiplier of “constrained revenue maximization” and “constrained output maximization”
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- Consider the following linear demand function where QD = quantity demanded, P = selling price, and Y = disposable income: QD = -36 - 2.1P + .24Y. The coefficient of Y (i.e., .24) indicates that (all other things being held constant): * for a one percent increase in disposable income, quantity demanded would increase by 0.24 percent for a one unit increase in disposable income, quantity demanded would increase by 2.1 units for a one percent increase in disposable income, quantity demanded would decline by 2.1 percent for a one percent increase in disposable income, quantity demanded would decline by 0.24 percentThe inverse demand function of a group of consumers for a given type of widgets is given by the following expression: π=−10q+2000 $ ( I ) where q is the demand and π is the unit price for this product. A. Determine the maximum consumption of these consumers. B. Determine the price that no consumer is prepared to pay for this product. C. Determine the maximum net consumers’ surplus. Explain why the consumers will not be able to realize this surplus. D. For a price π of 1000 $/unit, calculate the consumption, the consumers’ gross surplus, the revenue collected by the producers, and the consumers’ net surplus. E. If the price π increases by 20% (The new price π=1200), calculate the change in consumption and the change in the revenue collected by the producers. F. What is the price elasticity of demand for this product and this group of consumers when the price π is 1000 $/unit. G. Derive an expression for the gross consumers’ surplus. H. The supply function for the widget…Using a linear specification, you estimate your demand curve to equal Q=10-5P+20C+2A, where • Q = the quantity demanded of your product • P = the price of your product • C = college-ratio, which is the percentage of the local population that attends college. For instance, C=0.10 would indicate 10% of the local population attends a college. • A = digital advertising spend (in thousands of dollars) What is your demand elasticity with respect to the college-ratio when your price is $5, your digital advertising spend is $100,000 (i.e. A=100), and the college-ratio equals 0.25? a. εQ,C=0.0013 b. εQ,C=0.0263 c. εQ,C=20 d. εQ,C=15200
- Harding Enterprises has developed a new product called the “Quest Simulator (QS)”. The market demand for this product is given as follows: Q = 240 - 4P. If QS is priced at $40, what is the point price elasticity of demand? Is demand elastic or inelastic? What is the maximum amount that consumers are willing to pay for the quantity demanded at the price of $40? (hint: it includes both the total expenditures and the consumer surplus) If the price of QS is increased slightly from $40, what will happen to the total expenditure on the product? What will happen to the consumer surplus? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Sales are the function of advertising in The Dawn and Diva Magazine (X, Y). S = XY2 If the price of advertising in The Dawn and Diva Magazine is Rs.5 and Rs.10 respectively. The total budget for advertising is Rs.105. For maximizing the sales of Dawn and Diva Magazine find out the best combination of advertisements in newspapers and magazines by using the Lagrangian multiplier. please provide a complete solution with all the steps including formulas and proper workingThe consumer demand for a given product (where x represents number of units and p represents price is $) is given by the function x= (45-3p)2 Using the concept of Elasticity of Demand, determine the price that the product should be sold at to maximize revenue. Round to the nearest tenth.
- According to studies undertaken by the U.S. department of agriculture, the price elasticity of demand for cigarettes is about +0.5. Suppose a major brokerage firm advised its clients to buy cigarette stock under the assumption that, if consumer income rise by 50 percent as expected over the next decade, cigarette sales would double. Based on the fundamental economic principles on income elasticity of demand, a reasonable reaction to this investment advice would be?Sales are the function of advertising in The Dawn and Diva Magazine (X, Y). S = XY2 If the price of advertising in The Dawn and Diva Magazine is Rs.5 and Rs.10 respectively. The total budget for advertising is Rs.105. For maximizing the sales of Dawn and Diva Magazine find out the best combination of advertisement in newspapers and magazines by using Lagrangian multiplier.The weekly demand function for a particular product is q=f(p)=2400-15p. Where q is stated in units and p is stated in dollars. Determine the quadratic total revenue function, where R is the function of p. What is the concavity of the function? What is q intercept? What does total revenue equal at a price of 60 dollars.
- Q1. Derive the Marshallian demand and indirect utility function for ?(?,?)=(0.3?‾‾√+0.7?√)2u(x,y)=(0.3x+0.7y)2. Q2. Derive the Hicksian demand and the expenditure function for ?(?,?)=(0.3?‾‾√+0.7?√)2u(x,y)=(0.3x+0.7y)2.The demand equation for a firm’s product has been estimated as Ln Qx = 7.3 – 2 Ln Px + 0.5 Ln I + 0.25 Ln Py - 1.5 Ln Pz, where Qx represents unit sales of brand X, Px is the price of brand X, I is per-capita income, Py is the price of brand Y, and Pz is the price of brand Z. (A)Write this demand equation in its multiplicative form. (B) What is the price elasticity of demand for brand X? is demand price elastic or inelastic? (C)What is the income elasticity of demand for brand X? What type of good is brand X?The demand equation for a firm’s product has been estimated as Ln Qx = 7.3 – 2 Ln Px + 0.5 Ln I + 0.25 Ln Py - 1.5 Ln Pz, where Qx represents unit sales of brand X, Px is the price of brand X, I is per-capita income, Py is the price of brand Y, and Pz is the price of brand Z. (A)Write this demand equation in its multiplicative form. (B) What is the price elasticity of demand for brand X? is demand price elastic or inelastic? (C)What is the income elasticity of demand for brand X? What type of good is brand X? (D)What is the cross-price elasticity of demand for brand X in relation to the price of brand Y? What is the relationship between brand X and brand Y? (E) What is the cross-price elasticity of demand for brand X in relation to the price of brand Z? What is the relationship between brand X and brand Z? (F) What effect will an increase in Px by 10% have on the firm’s total revenues? (G)What is the total effect will an increase in Px by 10%, a decrease in I…