Question

Problem 5 This exercise takes you through how to caleulate equilibrium GDP and the multiplier for the 3-sector moel. You are given the following information: 51 Substitute the tax function into the consuanption function to obtain an oquation where consumption is some function of Y Answer 52 Write out the equation for PAE for the 3-sector model and indicate what is for equilibrium Answer 53 Now substitute the result from (5.1) and the values for G and given above, into the equation for PAE and use the equilibeium condition to solve for equilibrium Y Ansner 5.4 What is the size of the multiplier? Answer .5 Suppose the exogenous component of taxes is reduced from 20 to 10 Calculate the change in equilibeium GDP Answer

Answer 1

5.1 Consumption function C = 200 + 0.85(Y - 20 - 0.2Y) or C = 200 + 0.85(0.8Y - 20). This gives C = 183 + 0.68Y

5.2 PAE = C + I + G

For short run equilibrium, PAE must be equal to Y (income)

5.3 PAE = 183 + 0.68Y + 50 + 100

PAE = 333 + 0.68Y

Y - 0.68Y = 333

Y = 1040.625

5.4 Size of multiplier = 1/1-MPC(1-t) = 1/1-0.86 = 3.125

5.5 New equation for PAE = 200 + 0.85(0.8Y - 10) + 50 + 100 or PAE = 341.50 + 0.68Y. This gives Y = 1067.18

Change in GDP = 26.56