Suppose There Are Two Goods, Consumption C with Price P

Essay

Suppose there are two goods, consumption C with price p = 1 and leisure L with price w = 8. The endowments of the two goods are given by C₀ = 0 and L₀ = 2 4. The utility function is U(C,L)= logC + 2logL.
i)How much labour should be supplied and how much consumption should be chosen?
ii)Using all the information given above (except w = 8), show that the amount of labour supplied will be the same regardless of the wage rate. What must be true about income and substitution effects for this to occur?