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 .