(a) Explain the differences between a behavioral equation, a definition, an identity and an equilibrium condition. Provide an example for each type of relationship. (b) Solve the goods market equilibrium condition for production, i. e., solve the fol- lowing equation for y Y = co + C (Y T) ++ Subsequently, determine the following partial derivatives: Y y y Y y al' OG' aco' dc T The first three partial derivatives are referred to as tax multiplier, investment multiplier and government expenditure multiplier, respectively. Determine the sign of each of the multipliers.