Answer to Question #208650 in Macroeconomics for Juhi

Question

A primitive economy depends upon imports M=M(t) to sustain its recently acquired technology. Exports X=X(t) are a fraction of the output Y=Y(t), i.e. X=aY (0<a<1). And output is thought to grow according to the law dy/dt-bM (0<b<1). Current debt satisfies dD/dt=rD+M-X where r is the constant interest rate. Creditors have in mind to allow debt growth to be exactly balanced by export growth, i.e. dD/dt=dx/dt. Find a differential equation for D by eliminating M, X, and Y and hence determine the behaviour of debt. What initial dept to output ratio Do/Yo allows steady state debt? [Hint: D(t)-Do-X(t)-X=X-aY₁ Do and Xo are the initial values]

Answer 1

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