Question

Consider the following behavioral equations: C = c0 + c1YD, T = t0 + t1Y, YD = Y – T, I = b0 + b1Y, G is constant. Assume that t1 is between 0 and 1.
a. Solve for equilibrium output.
b. What is the multiplier? Explain what the following symbols in the equation stand for. c0, c1, t0, t1, YD, b0 and b1.
c. How will a drop in all C, I and G affect inflation? Illustrate this in DIAGRAM with AD and long-run AS.

Answer 1

Answer on Question #66480 – Economics – Macroeconomics

Question

Consider the following behavioral equations:

$$\begin{array}{l} C = c0 + c1YD, \\ T = t0 + t1Y, \\ YD = Y - T, \\ I = b0 + b1Y, \\ G \text{ is constant.} \\ \end{array}$$

Assume that t1 is between 0 and 1.

a. Solve for equilibrium output.

b. What is the multiplier? Explain what the following symbols in the equation stand for. c0, c1, t0, t1, YD, b0 and b1.

c. How will a drop in all C, I and G affect inflation? Illustrate this in DIAGRAM with AD and long-run AS.

Solution

a) $Y = C + I + G = c0 + c1(Y - t0 - t1Y) + b0 + b1Y + G = c0 + c1Y - c1t0 - c1t1Y + b0 + b1Y + G$

$$\begin{array}{l} Y - c1Y + c1t1Y - b1Y = c0 - c1t0 + b0 + G \\ Y = (c0 - c1t0 + b0 + G) / (1 - c1 + c1t1 - b1) \\ \end{array}$$

b) Multiplier is the factor by which increase in total output are greater than the change in spending that caused it.

c0 – autonomous consumption

c1 – marginal propensity to consume

t0 – lump-sum tax

t1 – rate of income tax

YD – disposable income

b0 – autonomous investment

b1 – marginal propensity to invest

c) Drop in all C, I and G negatively affects on aggregate demand: AD1 shifts to AD2. Price falls accordingly from P1 to P2.

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