4. Given U = (x + 1)(y + 4) and P, = 2, P, = 3, and B = 226.• Write the Lagrangian function.• Find the optimal levels of purchase x" and y".Is the second-order sufficient condition for maximum satisfied• How does the optimal utility U depend on B?

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Answered: 4. Given U = (x + 1)(y + 4) and P, = 2,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 1RQ

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4. Zack consumes mangosteen(m) and chalta (c) and his satisfaction function from consumingthese fruits is given by S = (m+2)(y+1) The price of mangosteen Pm = 4 and the price of chalta, Pc = 6. He has 130 taka to spend on these fruits.a. Write the Lagrangian function.b. Find the optimal levels of purchase for mangosteen and chalta.c. Use bordered Hessian to prove that the second order condition is satisfied.d. What is the value of the Lagrangian multiplier? Show that if the budget is increased by one Taka,the increase in his satisfaction level is equal to the value of the Lagrangian multiplier.
Assume (FT2 = FT1 (1 + TIT2) + T1CT2 is the equilibrium situation. Also assume that T2- T1 is one year, that T1CT2 = $1 and that TirT2 = 10%. %3D Assume the initial prices are FOT1 = 100 & FOT2 = 133. A trader goes long the FT1 contract and short the FT2 contract believing these are not equilibrium prices and that he will profit when they adjust to equilibrium. Say the next day, t+ 1, the t+1FT1 price moves to 115 and t+1FT2 adjusts to an equilibrium price. If the trader round trips his positions on day t+1, what is his profit or loss on the FT2 position? profit of 11 loss of 11 cannot be determined from the information given profit of 5.5

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4. Given U = (x + 1)(y + 4) and P, = 2, P, = 3, and B = 226. %3D •Wnite the Lagrangian function. Find the optimal levels of purchase x and y". Is the second-order sufficient condition for maximum satisfied How does the optimal utility U' depend on B?