Distinguish between ordinal and cardinal utility approach in consumer behaviour. Explain the assumptions of cardinal utility.

Hapa kuna hatua za kutoa kazi za mahitaji ya x_1 na x_2: Step 1: Weka kazi ya Lagrangian. Kazi ya Lagrangian inajumuisha kazi ya matumizi na kizuizi cha bajeti. L(x_1, x_2, ) = x_1 x_2 - (P_1 x_1 + P_2 x_2 - M) Step 2: Tafuta masharti ya mpangilio wa kwanza (First-Order Conditions - FOCs). Tunachukua derivatives za sehemu ya L kwa heshima ya x_1, x_2, na na kuziweka sawa na sifuri. 1. L x_1 = x_2 - P_1 = 0 x_2 = P_1 (Mlinganyo 1) 2. L x_2 = x_1 - P_2 = 0 x_1 = P_2 (Mlinganyo 2) 3. L = -(P_1 x_1 + P_2 x_2 - M) = 0 P_1 x_1 + P_2 x_2 = M (Mlinganyo 3) Step 3: Tatua mfumo wa milinganyo. Kutoka Mlinganyo 1 na 2, tunaweza kutoa : Kutoka (1): = (x_2)/(P_1) Kutoka (2): = (x_1)/(P_2) Sasa tunalinganisha maneno haya mawili ya : (x_2)/(P_1) = (x_1)/(P_2) P_2 x_2 = P_1 x_1 Tunatenga x_2: x_2 = (P_1 x_1)/(P_2) Step 4: Badilisha x_2 kwenye kizuizi cha bajeti. Badilisha usemi wa x_2 tuliojipatia kwenye Mlinganyo 3: P_1 x_1 + P_2 ((P_1 x_1)/(P_2)) = M P_1 x_1 + P_1 x_1 = M 2 P_1 x_1 = M Sasa tunatenga x_1 ili kupata kazi ya mahitaji ya x_1: x_1 = (M)/(2 P_1) Step 5: Badilisha x_1 ili kupata kazi ya mahitaji ya x_2. Badilisha kazi ya mahitaji ya x_1 tuliyoipata kwenye usemi wa x_2: x_2 = (P_1)/(P_2) ((M)/(2 P_1)) x_2 = (M)/(2 P_2) Kazi za mahitaji ni: x_1 = (M)/(2 P_1) x_2 = (M)/(2 P_2) Tuma swali linalofuata 📸