The following information describes an open economyC =60 +0.8Yd ; Yd = Y-T+ TR ; I= 100-5i ; i= 6; G =76; T =; 15; TR =60; X= 70; M= 12+0.2Y; i. Derive the IS equationli. Calculate equilibrium level of incomeiii. Calculate #foreign_trade_multiplieriv. At equilibrium whether the country enjoy a trade surplus or deficit? What is the size of trade surplus/deficit?v. If the government's expansionary monetary policy reduces the interest rate to 4 percent; what would be the impact of this policy change on the economy?

i. Derive the IS equation

The IS equation is derived from the equilibrium condition for the goods market, which is Y = C + I + G + (X - M).

First, substitute the given equations into the equilibrium condition:

Y = [60 + 0.8(Y - T + TR)] + [100 - 5i] + G + [X - (12 + 0.2Y)]

Substitute the given values:

Y = [60 + 0.8(Y - 15 + 60)] + [100 - 5*6] + 76 + [70 - (12 + 0.2Y)]

Simplify the equation:

Y = 60 + 0.8Y - 12 + 48 + 100 - 30 + 76 + 70 - 12 - 0.2Y

Combine like terms:

0.6Y = 300

Solve for Y:

Y = 500

So, the IS equation is Y = 500.

ii. Calculate equilibrium level of income

The equilibrium level of income is the value of Y that satisfies the IS equation, which we found to be Y = 500.

iii. Calculate #foreign_trade_multiplier

The foreign trade multiplier is the change in equilibrium income that results from a one-unit increase in net exports. It is calculated as 1/(1 - marginal propensity to consume + marginal propensity to import).

In this case, the marginal propensity to consume is 0.8 and the marginal propensity to import is 0.2, so the foreign trade multiplier is 1/(1 - 0.8 + 0.2) = 2.5.

iv. At equilibrium whether the country enjoy a trade surplus or deficit? What is the size of trade surplus/deficit?

A trade surplus occurs when exports exceed imports, while a trade deficit occurs when imports exceed exports. In this case, exports (X) are 70 and imports (M) are 12 + 0.2Y. At the equilibrium level of income (Y = 500), imports are 12 + 0.2*500 = 112. Since exports exceed imports, the country has a trade surplus of 70 - 112 = -42, which is a deficit of 42.

v. If the government's expansionary monetary policy reduces the interest rate to 4 percent; what would be the impact of this policy change on the economy?

A reduction in the interest rate would increase investment (I), as the cost of borrowing decreases. Using the given investment function I = 100 - 5i, if i decreases to 4, then I increases to 100 - 5*4 = 80. This increase in investment would shift the IS curve to the right, leading to an increase in the equilibrium level of income. This would stimulate economic growth and potentially reduce unemployment. However, it could also lead to inflation if the economy is already near its capacity.