for the constrained optimisation problem below, find the demand functions and the lagrangian multiplier. interpret the multiplier. max U(x, y)=4x 2+ 3y ² subject to 3x + 4y=100
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- 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 workingSales 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.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).
- 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.Create a full optimization problem with constraints and employ the Lagrange multiplier technique. One on the consumer side with constraints (utility maximization) and one on the producer side (either production / cost minimization , and or profit maximization.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.
- 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?A Lagrangian equation for total profit was solved, giving a Lagrangian multiplier of 94 and an output of 28. Which of the following statements is/are true? (i) If output increases by 100%, total profit will be increased by 94%. (ii) The marginal profit is exactly 94 when Q = 28. (iii) Profit will be maximised when output is at 94. (iv) If an additional item costs less than 94, it should be produced. a.(i) and (iv) only b.None of these other available answer choices is correct c.(i) only d.(ii) and (iii) only e.(iii) only
- 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 monthSuppose we have a demand model for good x. It is modelled as: Q=1450-0.38p-0.61p_y-0.0086I where I is the consumers’ average disposable income How would the consumer perceive the two goods, and with respect to consumers’ disposable incomes how would they perceive good x? Substitutes goods; normal goods Complements goods; normal goods Substitutes goods; Inferior goods Complements goods; Normal goods None of the above.