1.2.2 The constraints for the consumer are given by, PIC1 + P2C2 Sy ReA MIAM P1, P2, y > 0 CAUOH S : JMIT C1, C2 2 0 Given the objective function from 1.2.1 and the constraints provided, construct the Lagrangian for the consumer's problem. 90 10 SHOTARECOM JAMA [2] 1.2.3 Calculate the first order partial derivatives of the Lagrangian with respect to C1, C2 and the Lagrangian multiplier. iso dedbog aidsminsigong-non vine 7008 BHT RO [2] wars nisambluone noy emil 1.2.4 Given prices p1 = 5, p2 = 2 and income y = 20, calculate the values for c, and C2 that maximises utility. [3]1.2 We have an economy with two goods and the following components, Utility function u(C1, C2) Exogenous income y Price vector (P1, P2) The inputs into the utility function are two consumption goods. These two goods form part of the consumption bundle. The explicit utility function for the consumer is a Cobb-Douglas utility function, where u (C1, C2) = C1 -CZ 1 /2 1.2.1 Write out the objective function for the consumer. [2]