Final answer:
To find the equilibrium, we use two methods that involve setting aggregate expenditure equal to national income or using the GDP multiplier to calculate the change in government spending needed to reach a potential GDP of $3,500.
Step-by-step explanation:
To find the equilibrium for an economy using the provided information and determine the government spending changes needed to reach a potential GDP, two methods can be utilized.
The first method involves directly substituting values into the equilibrium condition that aggregate expenditure (AE) equals the national income (Y), while the second method uses the multiplier to calculate the required change in government spending.
Firstly, we calculate AE as follows:
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- AE = C + I + G + X - M
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- AE = 400 + 0.85(Y - T) + 300 + G + 500 - 0.1(Y - T)
Given that T = 0.25Y, we substitute T in the equation and set AE equal to Y to solve for G. As for the multiplier approach, it is derived from the marginal propensity to consume and the tax rate, which impacts the initial change in spending required to reach the potential GDP.
In essence, to reach a potential GDP of $3,500, changes in government spending are necessary. This change can be calculated by figuring out the level of spending that would equate AE to the desired GDP or by determining the GDP multiplier and applying it to adjust G accordingly.
The point elasticity of a demand equation is a measure of how sensitive the quantity demanded is to changes in price or income. In this scenario, the demand equation for government expenditures is log(G) = γlog(t) + log(Y) + log(M). The estimate for γ is 0.8. To find the point elasticity at the median, we plug in the median values G = $6.2 billion and Y = $108,000 into the equation.
Point elasticity = (dlog(G)/dlog(t)) * (t/G) = γ = 0.8.