Consider the goods market model with constant investment. Consumption is given b

Question

Consider the goods market model with constant investment. Consumption is given by C-co +CCYT and I, G, and T are given. Solve for equilibrium output Y(Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts E.g, a subscript can be created with the character.) What is the value of the multiplier for a change in autonomous spending? Multiplier-(Properly format your expression using the tools in the palette) Now let investment depend on both sales and the interest rate Consumption is given by CC(Y-D For the above model, solve for the goods market equilibrium output. Y (Properly format your expression using the tools in the palette.) When investment depends on income and the interest rate, the effect of a change in autonomous spending on output at a given interest rate is bigger than the effect when investment is autonomous because 1-Cassming , +b, s1. 1-c1-b c1 > by, assuming c1 + b1

Explanation / Answer

Y = C + I + G

= c0 + c1(Y-T) + I + G

(1-c1)Y = c0 - c1T + I + G

which gives Y = 1/(1-c1)[c0 - c1T + I + G]

For a change i autonomous spending, the multiplier is given by:

Multiplier = 1/(1-c1)

Now, given the new equation for investment, the new equilibrium Y is given as:

Y = C + I + G

= c0 + c1(Y-T) + b0 + b1Y - b2i + G

= c0 + b0 + (c1 + b1)Y - c1T - b2i +G

Thus, Y = 1/(1-c1 - b1)[c0 + b0 - c1T - b2i +G]

When investment depends onincome andinterest rate, the effect of a change in auutonomous spending on output at a given interst rate is bigger than the effect when investment is autonomous because:

(A) 1/(1-c1 - b1) > 1/(1-c1), assuming c1 + b1 is less than 1.

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