Question

Assume a consumer with the utility function
U = U(X, Y) = (X + 2)(Y + 1)
M = 95, Px= 10, and Py= 5
A Set up the consumers’ budget constraint
a. Set up the constrained maximization problem, and derive the first-order conditions.
b. Find the amounts of goods X and Y the consumer will purchase in equilibrium

Answer 1

A) 10X+5Y=95; => 5y=95-10x; => y=19-2x

B) (x+2)(y+1)→max

y=19-2x

C) (x+2)(19-2x)→max

19x+38-2x2-4x→max

(-2x2+15x+38)’=0

-4x+15=0

X=3.75

Y=19-2*3.75=11.5