Please solve and include steps

Let the following equations represent a model of an economy.

$1.$ Y $=$ C $+$ I $+$ G $+$ X $-$ M

$2.$ C $=100+0\mathrm{.}8$Y

$3.$ I $=200$

$4.$ G $=250$

$5.$ X $=100$

$6.$ M $=50+0\mathrm{.}05$Y

a$.$ How much is equilibrium income and open economy multiplier?

b$.$ Is the balance of payments in surplus or deficit?

c$.$ By how much do we need to change G in order to have a balance of payments

equilibrium?

d$.$ What will be the impact on Y and the trade balance if exports increase by $10($say

due to an increase in foreign demand$)$ and Fed cuts the discount rate which results

in an increase in investment by $10$ and an increase in autonomous consumption by

$10.$

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