a) 1) Y: The variable Y denotes the Gross Domestic Product(GDP) or Income which is defined as the money value of all goods and services produced within the domestic boundaries of a country in a particular year.

2) C: The variable C denotes Consumption Expenditure which consists of private expenditures(houshold final consumption expenditure) in the economy.

3) I: The variable I denotes Investment which includes business investment in equipment. Spending by households excluding government on new houses is also known as investment. However, investment in financial assets falls outside the purview of GDP(Y)

4) G: The variable G denotes Government Spending which is the sum of government expenditures on final goods and services. It includes salaries of public servants, purchase of weapons for the military, and any investment expenditure by a government.

5) T: The variable T denotes Taxes which are deducted from the income to finally arrive at the disposable income which is used for consumption.

6) M: The variable M denotes the Nominal Money Supply as supplied by the central bank of the country.

7) P: The variable P denotes the Price Level in the economy.

Therefore, M/P denotes the real money supply which would be equal to the money demand

b) The Investment- Savings(IS) curve denotes all combinations of interest rates and output at which the goods market is in equilibrium. We will make use of the equation Y=C+I+G to derive the IS curve.

Y=C+I+G ------(1)

Substituting the values of C,I and G in equation 1, we get

Y=400 + 0.5(Y-T)+250 -5r+ 500

Solving the brackets and taking variable Y to the left hand side we get,

Y-0.5Y=400-0.5T+250-5r+500

0.5Y=1150-5r-0.5T

Substituting T=1500 from the question,we get

0.5Y=1150-5r-0.5*1500

 

0.5Y=1150-5r-750

0.5Y=400-5r

Therefore, Y=400/0.5-5r/0.5

Y=800-10r is the IS curve equation

 

c) The Liquidity-Money (LM) curve shows all combinations of interest rate and output at which the money market is in equilibrium. The money market is in equiibrium when,

Money Demand= Money Supply

Therefore, (M/P)^d= 4Y-40r ------(2)

Substituting the value of M and P in equation 2, we get,

3600/3=4Y-40r

1200=4Y-40r

Therefore, 4Y=1200+40r

Y=300+10r is the LM curve equation

 

d) In order to derive the equilibrium level of income and the interest rate, the goods market equilibrium (IS) should be equal to the money market(LM) equilibrium.

Therefore, equating IS=LM, we get

800-10r=300+10r

On solving,

500=20r

Therefore, r=25.

Substituting, r=25 in the IS curve equation, we get

Y=800-10*25

Y=800-250

Y=550

Equilibrium Income,Y=550 and Equilibrium Interest Rate,r=25

please see the attached file for the complete solution.