$4*.$ Suppose the free floating exchange rate between the U$.$S$.$ dollar and Yuan $$1=4$ Yuan, i$.$e$.,S(\frac{\text{Y}\text{u}\text{a}\text{n}4}{\text{\$}}).$ Assume that China wants to maintain a weaker Yuan at the rate of $$1=8$ Yuan, i$.$e$.,S(\frac{\text{Y}\text{u}\text{a}\text{n}8}{\text{\$}}).$

a$)$ What actions by the central bank of China is required to make this weaker rate to be binding $($to be an effective price floor$)?$ Draw a completely labeled graph, and explain possible action$($s$)$ by China's central bank, and briefly, explain the macroeconomic impacts in China.

b$)$ Assume after China supported its price floor, with action$($s$)$ you describe in $($a$)$ above, political uncertainty in the rest of the world causes capital inflow into the U$.$S$.($$ country$)$ economy. Show with graph and explain consequences of this capital inflow into the U$.$S$.$ market on the China's central bank policy for maintaining its rate at $S(\frac{\text{Y}\text{u}\text{a}\text{n}8}{\text{\$}}).$

Please include graphs.