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The IS Curve.

The demand for consumer goods and the demand for producer goods vary inversely with the rate of interest r. Therefore, the c + i + g curve as a function of national income, y, shifts upward as the rate of interest, r, decreases. Consequently, a lower rate of interest requires a higher level of national income for equilibrium in the commodity market. The IS curve is the locus of interest rates and national incomes implicit for equilibrium in the commodity market, an inverse relation between the rate of interest and national income.

In the diagram below, the top panel shows the three c + i + g curves as a function of national income, y, for three values of the rate of interest, r.

The intersections of the c + i + g curves with the 45 degree line, yields the levels of national income, y, that will equilibrate the product market at the three rates of interest.

The c + i + g curve as a function of r and y is:

c + i + g = 427.5 + 0.746*y - 60*r + 2*r²

For r = 6, c + i + g as a function of the national income y is:

c + i + g = 139.5 + 0.746*y

    This red c + i + g curve intersects the yellow 45 degree line at y = 549.21.

The pair (r, y) = (6, 549.21) lies on the IS curve in the bottom panel.

c + i + g = 248.95 + 0.746*y

    This blue c + i + g curve intersects the yellow 45 degree line at y = 980.08.

The pair (r, y) = (3.35, 980.08) lies on the IS curve in the bottom panel.

c + i + g = 315.5 + 0.746*y

    This yellow c + i + g curve intersects the yellow 45 degree line at y = 1242.13.

The pair (r, y) = (2, 1242.13) lies on the IS curve in the bottom panel.