Construct a table using the given consumption functions.

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Chapter 13, Problem 13.1CC

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Construct a table using the given consumption functions.

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You are given the following data concerning Freedonia, a new republic. 1) Consumption is 200 when income is zero and the marginal propensity to consume is 0.6 out of every dollar increase in income 2) Investment function: I = 200 3) AE ≡ C + I 4) AE = Y Derive the savings function? Graph equations 3) and 4) and solve for equilibrium income (Y). Suppose equation 2) is changed to I = 150. What is the new equilibrium level of income (Y)? By how much does the $50 decrease in planned investment change equilibrium income? What is the value of the tax multiplier?

Imagine this economy has a 10% tax on income. The following are exogenous (not directly affected by income): G = 11 I = 4 X = M = 0 The consumption function is: C = k + cY, where k = 3, c = 0.8 Now we have to take that tax into account. Here is a way to think about it: Look at the consumption function. It says if you give me one more dollar of income I will spend 80 cents of it (mpc = 0.8). BUT I can only spend what I receive. I can only spend my after-tax or disposable income. With a 10% tax, I don't receive Y I receive 90% of Y or Y*(1-t) where t = 10% or 0.1. Let's define disposable income as Yd where Yd = Y*(1-t). Therefore we restate our consumption function as C = k + cYd Now we have, in this case, C = k + cYd or C = 3 + 0.8Yd or C = 3 + 0.8*(Y*[1-0.1]) or C = 3 + 0.72Y. Now what is the equilibrium GDP? Give the answer to ONE decimal place.

The following are exogenous (not directly affected by income): G = 11 I = 4 X = M = 0 The consumption function is: C = k + cY, where k = 3, c = 0.8 Now we have to take that tax into account. Here is a way to think about it: Look at the consumption function. It says if you give me one more dollar of income I will spend 80 cents of it (mpc = 0.8). BUT I can only spend what I receive. I can only spend my after-tax or disposable income. With a 10% tax, I don't receive Y I receive 90% of Y or Y*(1-t) where t = 10% or 0.1. Let's define disposable income as Yd where Yd = Y*(1-t). Therefore we restate our consumption function as C = k + cYd Now we have, in this case, C = k + cYd or C = 3 + 0.8Yd or C = 3 + 0.8*(Y*[1-0.1]) or C = 3 + 0.72Y. Now what is the equilibrium GDP?