Suppose the United States economy is represented by the following equations:
Z = C + I + G C = 500 + .5YD T = 600 I = 300
YD = Y - T G = 2000
a. Given the above variables, calculate the equilibrium level of output. Hint: First specify (using the above numbers) the demand equation (Z) for this economy. Second, using the equilibrium condition, equate this expression with Y. Once you have done this, solve for the equilibrium level of output. Using the ZZ-Y graph (i.e., a graph that includes the ZZ line and 45-degree line with Z on the vertical axis, and Y on the horizontal axis), illustrate the equilibrium level of output for this economy.
b. Now, assume that consumer confidence decreases causing a reduction in autonomous consumption (c0) from 500 to 400. What is the new equilibrium level of output? How much does income change as a result of this event? What is the multiplier for this economy?
c. Graphically illustrate the effects of this change in autonomous consumption on the demand line (ZZ) and Y. Clearly indicate in your graph the initial and final equilibrium levels of output.
d. Briefly explain why this reduction in output is greater than (in absolute terms) the initial reduction in autonomous consumption.