For the first question how did they get 3Px in the denominator by adding (1/2+1/4)?

Economics 425 Homework 1 Lessons 1 and 2 1. Deriving Demand (9 points) Suppose an individual has the following characteristics: Utility=X"Y , which implies MUX=ax"-ly, MUy=BX"YB-1 where income M-500, a-1/2, B-1/4 a) Derive the formula for the demand curve for good X a ) Budget Constraint : M = X . PX + Y . Py From the condition of profit maximization PX Muy Py 13 x 0 * B - 1 Py a Y _PX B X Py Therefore , y= P . X - Px Py Inserting it into the budget constraint , we ofet At = X - PX + ( 12 , Xi BX ) . Py Py = * . PX + ( P . x . P x ) = X . Px ( 1+ 2 ) Thes , * = X - PX CITY ) Px . (Ol + B ) 7 This is the formulas for the demand curve for good x Inserting The values . M= SOO, OL = 2 , P = 4 X = 1000 P X " ( 2 + 4 ) 3 PX b) Graph the curve and plot the points when the price of X is P=100, P=50, P=25, P=10