Question

8. Investment and income This problem examines the implications of allowing investment to depend on output. Chapter 5 carries this analysis much further and introduces an essential relation-the effect of the interest rate on investment-not examined in this problem. a. Suppose the economy is char acterized by the following behavioral equations: Government spending and taxes are constant. Note that investment now increases with output. (Chapter 5 discusses the reasons for this relation.) Solve for equilib- rium output. b. What is the value of the multiplier? How does the relation between investment and output affect the value of the multiplier? For the multiplier to be positive, what condition must (c1 + b) satisfy? Explain your answers. c. What would happen if (c1 b)1? (Trick question. Think about what happens in each round of spending) d. Suppose that the parameter bo, sometimes called busines confidence, increases. How will equilibrium output be af- fected? Will investment change by more or less than the change in bo? Why? What will happen to national saving?

Answer 1

Y = C + I + C T = [1/ (1 + c_1 - b_1)] times [c_0 - c_1 T + b_0 + G] Including the b_1Y term in the investment equation increases the multiplier Increases in autonomous spending now creates a multiplier effect through two channels: consumption and investment For the multiplier to be positive, the condition c_1 + b_1 < is required When c_1 + b_1 is greater than one there is no multiplier effect When total spending exceeds one the formula is nonsensical The multiplier should be 1/(1 - c_1 - b_1) So, when c_1 + b_1 is greater than one the multiplier is negative, which does not make sense Another way of looking at this concept is saving must equal investment so in a closed economy c_1 + b_1 cannever be greater than one Output increases by b_0 times the multiplier Investment increases by the change in b_0 plus b_1 times the change in output The change in business confidence leads