Question

1. Alice has a fixed budget of $120 to purchase two goods. Let X and Y represent the quantity of goods X and Y purchased respectively. Price of X is $2, price of Y is $1, and her utility function is U= X²Y and her MRS = 2Y/X

1. Write down the budget line function
2. Write down the tangency condition
3. Calculate the optimal consumption bundle (X=    Y=   )
4. Draw a graph to show you results (including budget line, utility, and optimal consumption bundle with relevant numbers)
5. What is her maximized utility level?

Answer 1

Ans.

Aus. Budget (M) = $120 Price of good x = $2 fice of good Y=61 and MRS - 2Y the budget line function :- I Px. X + Py. Y=M S 2X + Y =}|2o © L 2x+y=120 Terngang condition, mes a 24 = ² nay Condition MRS Ty=x] o plaggin value of y into budget line function, we have 2x + x = 120 3x = 120 1 x 240 and 143.40] [:4=*] Hence, the optimal consumption bundle ee (x,y) (40,40)

8x+y=120 Budget line: x intercept - N Y intercept = 60 = 120 120 consumption bundle Y = 40 optimal A IC Ic \ BL 60 at x240 6 maximuun utility level at (x,y) = (40,40) U (40,40) = (40)2(40) [vky) = x2y] U (40,40) = 64,000