Question

1. Jason has $60 and wants to spend all his money on bread(X) and ham(Y) for lunch. As we know, he tends to consume 3 units of bread with every 2 units of ham. Suppose the price of goods are $2(X) and $7(Y) respectively. A. Write down Jason's utility function and budget constraint. B. Calculate Jason's optimal point. C. Show the optimal point in graph. From now on, Jason's preference changes but budget constraint doesn't. The new utility function is: U = 3x2+7Y2 + 6. D. Please calculate Jason's new optimal point. (Note: Using Lagrange Method)

Answer 1

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bndyrt epain 2.3y 60 60 = 6 Ond 3xk3 ЗУ 62 х Е Чот () 6 a,6) 10 () 2x 7Y 60 aul 2 x (6cad) 3 3x3 2 4 de onkuint 6 2X t7y -60

(-x - y) 3xt(-2x-7) 8x+y6 2x - 7y Furada ondihione 6x 2A X 14y 11 22 60 2X -7Y FABnand (i 6X 14 y 2 3 3 So X 2Y 3 oketiakey 60 2.2Y 3 4 Y b0 11

4Y 21y 4y 7y 3 3 60 25 y 3 y 4.2 25 5 2Y 3 2 x 2.4 4.8 Wewe iual foint X 4.8 and Y 7.2