1. Suppose the households in a hypothetical economy has the following consumption function C = a + cya Where Ya is the disposable income. The government in this economy imposes a tax rate of 0 < t < 1 to households' income (ex. A t = 0.10 means that 10% of households' income goes to tax payments). a. What is the equation that describes the disposable income Ya of households? b. What is the planned Expenditure Equation? Assume that government expenditure is exogenous and Investment function is given by the equation 1 = 1 - br Where r is the interest rate. c. Derive the equilibrium output Y* in the goods market and show that the multiplier in this model is ₁-c(1-t) d. How does c and the tax rate t affects this multiplier (e.g., what happens to multiplier if c increases cet.par or if tax rate increases, cet.par)?

ENGR.ECONOMIC ANALYSIS
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1. Suppose the households in a hypothetical economy has the following consumption function
C = a + cya
Where Ya is the disposable income. The government in this economy imposes a tax rate of
0 < t < 1 to households' income (ex. A t = 0.10 means that 10% of households' income goes
to tax payments).
a. What is the equation that describes the disposable income Ya of households?
b. What is the planned Expenditure Equation? Assume that government expenditure is
exogenous and Investment function is given by the equation
1 = 1 - br
Where r is the interest rate.
c. Derive the equilibrium output Y* in the goods market and show that the multiplier in this
model is ₁-1-t)
1-c(1-t)*
d. How does c and the tax rate t affects this multiplier (e.g., what happens to multiplier if c
increases cet.par or if tax rate increases, cet.par)?
Transcribed Image Text:1. Suppose the households in a hypothetical economy has the following consumption function C = a + cya Where Ya is the disposable income. The government in this economy imposes a tax rate of 0 < t < 1 to households' income (ex. A t = 0.10 means that 10% of households' income goes to tax payments). a. What is the equation that describes the disposable income Ya of households? b. What is the planned Expenditure Equation? Assume that government expenditure is exogenous and Investment function is given by the equation 1 = 1 - br Where r is the interest rate. c. Derive the equilibrium output Y* in the goods market and show that the multiplier in this model is ₁-1-t) 1-c(1-t)* d. How does c and the tax rate t affects this multiplier (e.g., what happens to multiplier if c increases cet.par or if tax rate increases, cet.par)?
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