Math/Economics/Optimization problem
Suppose that given quantities x1 and x2 of two items, your
utility is given by u(x1, x2) = x2 + 5 - (x1 - 3)^2.
a Sketch a few level curves of u.
b Suppose your purchasing is subject to a budget
constraint, and the optimal purchase is given by (x1, x2) = (2, 8).
Give the equation of the level curve of u that corresponds to this
purchase.
c Graph the level curve from b and use your
drawing to sketch the budget constraint on your graph.
d Give the equation of the budget constraint and
explain its meaning in words.
A) level curves:
Red: utility level = 12
Blue: U = 5
Green : U = 20
Purple : U = 35
Black : U = 25
Part c)
Green colour : level curve , when U = 12
Blue coloured straight line : budget constraint & is tangent to (2,8)
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