$(5$ points$)$ In $2018,$ the Trump administration ordered tariffs on steel imports from many countries including China. Assume that China's central bank fixed its exchange rate with the US dollar at the time.

a$.$ Use the IS$-$LM$-$FX model to illustrate the short$-$run effects of this tariffs policy on China's output, nominal interest rate, and investment. Display a suitable diagram.

b$.$ Suppose the goal of macro policy is to stabilize output in the short run. What kind of fiscal policy would you recommend to the China's government?

c$.$ Can China replace the fiscal policy in Part $($b$)$ with monetary policy? Explain your reasoning. If you answer yes, explain what kind of monetary policy is desirable.

d$.$ Suppose China's central bank switched to a flexible exchange rate regime before $2018.$ Use the IS$-$LM$-$FX model to illustrate the short$-$run effects of the Trump administration's tariffs policy on China's output, nominal interest rate, exchange rate and investment in this case. Display a suitable diagram.

e$.$ Given your answers in Parts $($a$)-($d$),$ will you recommend China's central bank to adopt a flexible exchange rate policy? Explain your reasoning.

Please show me the whole process and explain why. Thank you so much! Have a good day!