Chapter 20: Problem 4

There is only one combination of income and the rate of interest at which both the goods and the money market are in equilibrium.

Short Answer

Expert verified

Answer: The equilibrium point in both the goods and the money market in macroeconomic models represents the intersection of the IS-LM curves, indicating that both markets are in balance. At this point, investment equals savings (goods market equilibrium) and the demand for money equals the money supply (money market equilibrium). It also helps determine the equilibrium interest rate and income level in the economy.

Step by step solution

Understanding the IS curve

The IS curve represents the relationship between the interest rate and the level of income at which the goods market is in equilibrium. This equilibrium occurs when the investment (I) and savings (S) are equal. The IS curve is negatively sloped, indicating that as the interest rate decreases, the level of income (Y) increases.

Deriving the IS curve

The IS curve is generally derived from the investment-saving and consumption function: I(r) = I0 - (i1 * r) S(Y) = -C0 + (c1 * Y) where I0 is autonomous investment, i1 is the investment sensitivity to the interest rate, C0 is autonomous consumption, and c1 is the propensity to save. Equating investment and saving to find the equilibrium, I0 - (i1 * r) = -C0 + (c1 * Y)

Understanding the LM curve

The LM curve represents the relationship between the interest rate and the level of income at which the money market is in equilibrium. This equilibrium occurs where the demand for money (L) equals the money supply (M). The LM curve is positively sloped, as when the interest rate decreases, the level of income (Y) must increase for the money market to be in equilibrium.

Deriving the LM curve

The LM curve can be derived from the money demand function: L(Y, r) = L0 + (l1 * Y) - (l2 * r) where L0 is autonomous money demand, l1 is the demand sensitivity to income, and l2 is the demand sensitivity to the interest rate. To find the equilibrium point in the money market, equate money supply (M) with money demand (L): M = L0 + (l1 * Y) - (l2 * r)

Finding the equilibrium point

To find the equilibrium point for both the goods and money markets, we need to solve for the interest rate (r) and income level (Y) that satisfy both the IS and LM curves simultaneously. This can be done by solving the two equations to eliminate one variable: From the IS curve, Y = (I0 + C0) / c1 + (i1 / c1) * r Substitute this expression for Y in the LM curve: M = L0 + (l1 * ((I0 + C0) / c1 + (i1 / c1) * r)) - (l2 * r) Now, solve for r: r = (M - L0 - l1 * (I0 + C0) / c1) / (l1 * (i1 / c1) - l2) Once the interest rate has been found, plug it back into the Y expression from the IS curve to find income: Y = (I0 + C0) / c1 + (i1 / c1) * r At this point (r, Y), both the goods market and the money market are in equilibrium.