Question

I'm having trouble figuring out the below portion of this problem.

The preferences of a typical Californian can be represented by the following utility function: U(21, 22) = a ln(x1) + (1 – a) ln(x2) Here, X1 and 22 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by Pi and P2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x1 < 50). Call this restriction a rationing constraint.

Answer 1

Date ашин; t и хи) - DELTA PO NO ni = electricity «Lu xj + (-) и , 12 = gasoline Rationing constrant i M45O. uneu : PI=P2=1, without rationing m=100 constraint - constrant solu to me problem, solu to me problem, max u (Mina) St. Mi + x2 = 100 x= xmluit (1-2) u (12) tr(100-x1-x2) de = x -d=0 dwI t = 14 - x=0 - 0 duz 12 dt = 100 - n1 - H220 - 12 0 using the equ 092 x = - Xx2= x1(1-2) 1-4 x2 using mis relation u equ 6 ni+R2 =100 alt 11-41 n =100 n = 100 = 1 = 1004 22 -(-6) 100

... optimal electricity 3 (x1=1004] Ratining constrait is : 24450 . ΠΟΣ so 100 x Į so x 25o = 0.5. ) 4 1/2 ... af at 10 , / assuming & is a posituie parameter, he rationing constraint is met of the optimal consumption of ett electricity will not be affected & will remain the same at a> 1 te me rationing constraint & not met will allow max. electie consumption to be лаt . Уt - о а и мека иаи .. Rationing constraint affect consumer's consumption of electricity (xi) when &t (1 100).