Consider the following numerical version of the IS-LM model:

C = 60 + 0.6Yd
I = 150 – 10i
YD = Y – T
T = 200
G = 250
Real money demand: (M/P)d = (40 + 0.1 Y – 10i)P
Real money supply (M/P)s = 80
P = 2
Where

Y is output, Yd is disposable income, C is consumption, I is investment, i is the interest rate, G is government expenditure, T is tax, P is the price level.

c) From the above information, find the equation for the IS curve in terms of Y, and the LM curve in terms of Y.

(d) Solve for the equilibrium interest rate and level of income.
(e) Solve for the equilibrium values of consumption and investment spending and use the results to verify that they are consistent with the level of income calculated in (d) above.

(f) If the government increases expenditure by 40 to 290, solve again for equilibrium levels of Y, i, C and I.

(g) Using diagrams, explain how the results of your calculation in (f) above of interest rates and output are consistent with the predictions of IS-LM theory.

I UNDERSTAND THAT I MAY HAVE ASKED TOO MUCH BUT I WOULD BE REALLY GLAD IF YOU COULD HELP ME ANSWER EVEN A FEW OF THOSE QUESTIONS. RESPONSES ARE APPRECIATED. THANKS IN ADVANCE.

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i have just come across this website i am not familiar with it thanks for the advice

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Sure, I'll be happy to help you with your questions! Let's tackle them one by one:

c) To find the equation for the IS curve in terms of Y, we need to equate aggregate output (Y) to aggregate expenditure (AE), which is the sum of consumption (C), investment (I), and government expenditure (G). In this case, AE = C + I + G.

Substituting the given equations for consumption and investment into the expression for AE, we get:
AE = (60 + 0.6Yd) + (150 – 10i) + G.

Next, we need to rewrite disposable income (Yd) in terms of output (Y). Given that YD = Y – T and T = 200, we have YD = Y – 200.

Substituting this into the equation for consumption, YD = 60 + 0.6(Y – 200), we can simplify it to:
YD = 60 + 0.6Y – 120 → YD = 0.6Y – 60.

Substituting YD into AE, we have:
AE = (60 + 0.6(0.6Y – 60)) + (150 – 10i) + G.

Simplifying this expression, we get:
AE = 0.6Y + 36 – 36 + 150 – 10i + G → AE = 0.6Y + 150 – 10i + G.

This is the equation for the IS curve in terms of Y.

Now, let's find the equation for the LM curve in terms of Y. The LM curve represents the equilibrium in the money market, where the real money demand is equal to the real money supply.

Given the real money demand equation: (M/P)d = (40 + 0.1Y – 10i)P, and the real money supply (M/P)s = 80, with P = 2, we can equate these to find the LM curve.

(M/P)d = (40 + 0.1Y – 10i)P → (40 + 0.1Y – 10i)2 = 80.

Simplifying this equation, we get:
80 + 0.2Y – 20i = 80 → 0.2Y – 20i = 0.

Dividing both sides by 0.2, we get:
Y – 100i = 0 → Y = 100i.

So, the equation for the LM curve in terms of Y is: Y = 100i.

d) To solve for the equilibrium interest rate and level of income, we need to find the point where the IS curve intersects the LM curve. By setting the equations for the IS and LM curves equal to each other, we can solve for Y and i.

Setting AE = Y = 0.6Y + 150 – 10i + G equal to Y = 100i, we have:
0.6Y + 150 – 10i + G = 100i.

Simplifying this equation, we get:
0.6Y = 110i – (150 – G).

Since we know G = 250, we can substitute this into the equation:
0.6Y = 110i – (150 – 250) → 0.6Y = 110i + 100.

Now, let's solve this equation for Y and i.