Standard macroeconomic model and implicit differentiation
A standard macroeconomic model for income determination in an open economy is
where . Here is an exogenous constant that denotes exports, whereas denotes the volume of imports. The function in (iii) is called an import function. By inserting (ii) and (iii) into (i), we obtain an equation that defines as a function of exogenous investment .
(a) Find an expression for by implicit differentiation. What is the likely sign of ? Discuss the sign of .
(b) Find an expression for .