Hello, May I know the difference between this 2 of MRT? because as u seen in the picture it says National Economy Problem and Social Welfare? Does this 2 equation solve in 2 different way? How do I solve to get MRT= -PA/PM,LA+LM=L? p.s. A and M are the two goods production sectors. Can You please help explaining it to me and show me how to solve it? Your answer will be making my day very wonderful.

Paragraph Styles National Economy Problem: Production Value Maximization 1) Given Prices; PA and PM max PA-YA+ PM-YM S.I. YA=f(LA), YM=g(LM), LA+LM=L First order condition of this problem derives MRT= - PA , LA+LM=L PM 2) Derive first order condition as MRT=MRS, LA+LM=L H (MRS stands for the marginal rate of substitution of social welfare function) This slope is equilibrium price ratio: MRT = MRS PM PA PA . YA 4 PM . YM = PA. XA + PM . XM = 1 United States