Question

1) Suppose an economy is characterized by the following equations. Y = C+/+G Y = 10,500 G = 800 TA = 1000 S = 1600+ 0.1(Y-TA) + 20001 1 = 600+ 0.20Y - 30001 Where Y is real GDP, G is government purchases of goods and services, S is total national savings, is the nominal rate of interest and I is total investment. There are no transfers in this economy and agents can only consume or save their income. a) What is the marginal propensity to consume in this economy? b) What is the equilibrium interest rate in this economy? c) Calculate the total level of savings and investment at this rate of interest. d) What is the total level of private consumption in this economy?

Answer 1

a) It is known that sum of marginal propensity to consume (MPC) and marginal propensity to save (MPS) is equal to 1, that is, MPC + MPS = 1. From the saving function, the MPS can be determined. So, the MPS is 0.1. Now, compute MPC as, MPC + MPS = 1 MPC = 1 - MPS MPC = 1 -0.1 = 0.9 Hence, the marginal propensity to consume is 0.9. b) At good market equilibrium, the quantity demanded is equal to the quantity supplied. The following conditions shows the goods market equilibrium: Y=C+I+G Or S=1 Since consumption is yet not know, use S =I identity to find equilibrium interest rate as follows: S=1 1600+ 0.1(Y-TA) + 2000i = 600+ 0.2Y - 3000i 1600+ 0.1(10,500 -1,000 + 2000i = 600+ 0.2(10,500)-3000i 1600 +950+ 2000i = 600+ 2,100-3000i 5000i = 150 i=0.03 or i = 3%

c) At 3%, the total level of savings is, S=1600+ 0.1(Y-TA + 2000i = 1600+ 0.1(10,500 - 1,000) + 2000(0.03) = 1600+950 + 60 S = 2,610 At 3%, the total level of investment is, I = 600 +0.2Y - 3000i = 600+ 0.2(10.500) - 3000(0.03) = 600 +2,100-90 1 = 2,610 d) Total level of private consumption in this economy is, Y = C +I+G 10,500 = C +2,610+800 C = 7,090