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 working

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 working

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.3P

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Q1) Sales are a function of advertising in newspapers and magazines (X, Y). S = XY2 The price of advertising in newspapers and magazines is Rs.5 and Rs.10 respectively. The total budget for advertising is Rs.105. For maximizing sales, find out the best combination of advertisements in newspapers and magazines by using the Lagrangian multiplier. (Hint: Make equation of the budget line with the help of the above information).
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 working
Sales are a function of advertising in newspapers and magazines (X, Y). 05 S = XY2 Price of advertising in newspapers and magazines are Rs.5 and Rs.10 respectively. The total budget for advertising is Rs.105. For maximizing the sales, find out the best combination of advertisement in newspapers and magazines by using lagrangian multiplier. (Hint: Make equation of budget line with the help of above information).
Ruby has the following utility function: U(X, Y) = X^3/4 , Y^1/4, where X is her consumption of food items, with a price of $10, and Y is her consumption of clothing items, with a price of $30. She plans to spend $360 on food and clothing over the next week. Using the Lagrange multiplier technique, determine the number of food and clothing items that will maximize Ruby's utility.
A consumer is maximising her utility function: U(x, y) = (x¹/³+y¹/³)³, subject to the budget constraint x + 3y = 100. (a) Set up the Lagrangian function of this utility maximisation problem and derive the first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate the Lagrange multiplier. (c) What are the utility maximising amounts of x and y if the budget constraint changes to x + 3y = 50? Also, calculate the Lagrange multiplier.
Price of advertising in newspapers and magazines are Rs.5 and Rs.10 respectively. The total budget for advertising is Rs.105. For maximizing the sales, find out the best combination of advertisement in newspapers and magazines by using lagrangian multiplier.
Consider U(q1,q2) = q1 + v(q2) where v' > 0 and v'' < 0. This utility function is called a quasi-linear utility function. Assume q1 is a numeraire. Find the demand function for q2. *What does v mean in this question? Also, could you solve this problem without using Lagrange multipliers? Thank you.
You are given the following utility function: ? = ?? The budget is K100 and the price of X is K2 while the price of Y is K5. a) Derive the demand for X and Y by the Lagrange multiplier method. b) What will be the demand when all the prices are doubled and the income is doubled? c) What is the utility when the budget is increased by K1?
1. Use the Method of Lagrange to solve this problem. To do so, construct the La- grangean function for this problem. Use λ1 as the Lagrange multiplier attached to the period 1 budget constraint and λ2 as the Lagrange multiplier attached to the period 2 budget constraint.
The utility derived by a consumer from the consumption of two commodities is given by the function U (A, B) = 0.5In (A) + 0.5 In (B) where A are the number of units of the first commodity consumed and B are the number of units of the second commodity consumed each month. A unit of the first commodity costs $8 and a unit of the second commodity costs $ 4 using the Lagrange multiplier method determine the optimal quantity of each of the commodities consumed each month given that consumer has $32 to spend on both commodities each month
Suppose that the economy of country 1 is characterized by the following behavioral equations: Variable Equation Consumption C=1234 +0.5 YD Investments I=1000 + 0.1 Y Government expenditures G= 100 Net exports Nx= 300-0.2 Y Where Y denotes the real GDP and YD denotes the disposable income (YD= Y-T). Suppose that the output gap in country is measured as -15000. What should be increase in government expenditure in order to close the gap and make the economy to reach its potential level of GDP?.
A consumer consumes two agricultural products: Red Meat, and Tomatoes according to the following utility function: U = RT That is, the total utility is the multiplication of the quantity consumed of the two products. Given that consumer's income is 210, price of R is 10, and the price of Tis 2, a)Write down the budget constraint (budget line equation) for this consumer. b)Determine the quantities that the consumer should consume of each of the two products c)Calculate the value of the lagrangian multiplier and derive the demand function for Red Meat and for tomatoes.