Standard macroeconomic model and implicit differentiation

A standard macroeconomic model for income determination in an open economy is

**(i)**

**(ii)**

**(iii)**

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 .