In: Economics
Suppose that U = XY . The prices of good X and good Y are $10 and $5, respectively. How many units of good X does the consumer buy if she has $1000 of income?
a) 10
b) 25
c) 50
d) 41
the consumer optimizes according to the following condition:
MRS = MUx/MUy = Px/Py
=> Y/X = 10/5
=>Y = 2X
=> X = Y/2
Budget equation is:
X*Px + Y*Py = Income
=> 10X + 5Y = 1000
Putting Y = 2X in the equation, we get
10X + 5*2X = 1000
=> 20X = 1000
=> X = 1000/20 = 50
Thus, the answer is (c) 50