Please answer all parts!

Question 9 {8 points) [8 marks] Remy's technology for producing omelettes {3] is represented by a: : v'i+ 1 where i is labor. He derives the following utility from his consumption of omelettes ( z) and his labor (I): u{::, i) = z 2?. Assume Remy is the only consumer and producer of omelettes in his household. Suppose the price of omelettes is set at 1. 1. [4 marks] Show that Remy consumes 1.5 omelettes at the Pareto efficient allocation. 2. [4 marks] Find the market equilibrium allocation and wage rate