Question

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.

Answer 1

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)