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The relationship between aggregate investment, autonomous investment, and the interest rate can be expressed with the formula: $$I = a_0 - a_1r$$. In this equation, $$I$$ represents the total investment, $$a_0$$ is the autonomous investment that is independent of the interest rate, $$r$$ is the interest rate, and the parameter $$a_1$$ measures the sensitivity of investment spending to changes in the interest rate.

Aggregate Investment Formula

Given the case study, calculate the change in the level of aggregate investment resulting from the central bank's policy action and briefly explain the economic reasoning behind this change.

Investment Response to Interest Rate Changes

An economy's investment behavior is described by the equation I = 250 - 50r, where I is aggregate investment in billions of dollars and r is the interest rate expressed as a percentage (e.g., an interest rate of 5% should be entered as 5). If the central bank raises the interest rate from 3% to 5%, what is the resulting change in aggregate investment? Show your calculation.

Calculating the Impact of an Interest Rate Change

Suppose the aggregate investment in an economy is initially described by the function I = 1000 - 50r, where I is total investment in billions of dollars and r is the interest rate in percent. A major technological breakthrough significantly boosts business confidence, causing firms to increase their planned investment by $200 billion at every interest rate level. What is the new aggregate investment function?

Shifts in Autonomous Investment

In the multiplier model, where aggregate demand ($$AD$$) is plotted against national income ($$Y$$), aggregate investment ($$I$$) is a component of $$AD$$. For any single aggregate demand curve, determinants other than income, such as the interest rate ($$r$$), are held constant. Consequently, the entire aggregate investment function, $$I = a_0 - a_1r$$, is incorporated as a fixed value within the vertical intercept (representing autonomous demand) of the aggregate demand curve. Any change in these determinants of investment, such as a change in the interest rate or in autonomous factors like expected profits, shifts the entire aggregate demand curve.

Integration of the Investment Function into the Aggregate Demand Curve

Consider an economy where the relationship between total investment (I) and the interest rate (r) is described by the equation: I = a₀ - a₁r. If businesses in this economy become significantly more sensitive to changes in the cost of borrowing, how would this be represented in the equation?

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