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Consider a Keynesian Consumption Function with Desired Consumption Equal to 0.9

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Consider a Keynesian consumption function with desired consumption equal to 0.9 Y,where Y is income.Government purchases are $1000,net exports are zero,and desired investment varies with real interest rate according to the following schedule:
rId5%$30004%35003%40002%4500\begin{array} { c c } r & I d \\5 \% & \$ 3000 \\4 \% & 3500 \\3 \% & 4000 \\2 \% & 4500\end{array}
Assume the interest rate adjusts so that the economy gets to equilibrium.Equilibrium output at full employment is $50,000.Find the values of consumption,investment,and the real interest rate at full-employment equilibrium.


Definitions:

Central Limit Theorem

A statistical theory stating that the distribution of sample means approximates a normal distribution as the sample size becomes large, regardless of the population's distribution.

Sampling Distribution

The probability distribution of a given statistic based on a random sample, essential in estimating the sampling variability.

Sample Mean

The average value of a sample, used as an estimate of the population mean.

Infinite Population

A hypothetical concept referring to a population of unlimited size, used as an assumption in certain statistical models.

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