Hey! I am currently trying to solve this question:

Suppose households preferences are described by the utility function U(C, l) = 2C 1/2 + 3l, where C stands for consumption of market goods l stands for leisure. The total number of hours available to the representative consumer is 1, and the market real wage is w. Output is produced using the production function Y = (Nd ) 1/2 . For simplicity, let us assume that there is no government, that is G = 0. The firm distributes a profit = 0 to the consumer.

1. Solve the consumer's problem and find the optimal values of C ? , l ? , and then deduce Ns .

PROBLEMS I AM RUNNING INTO:

1. I'm hoping for step by step on finding the budget constraint (since so little information is giving)
2. I am used to finding MRS with Cobb Douglas and seeing the two variables in the utility function multiplied and not added, so thats throwing me off too. I'm hoping you could give me a step by step on finding u/l and u/c.
3. After identifying the MRS and BC, can you show me how to find optimal Ns? I know Ns=Nd=N however I'm not sure how to get there.

THANKS <3