Running head: FINDING THE IS CURVE 1

Transcription

1 Running head: FINDING THE IS CURVE 1 Finding the IS curve for a hypothetical economy Emily Parkins Vrije Universiteit Brussel Author Note Research Paper for Introduction to Macroeconomics (Professor Luc Hens) 15 March 2018

2 FINDING THE IS CURVE 2 Abstract For a hypothetical economy described by a given set of structural equations, I use algebra to derive the demand for domestic final product. The equation shows that when income increases by US$1 billion, demand for domestic final product increases by US$0.6 billion. When the interest rate increases by 1 percentage point, demand for domestic final product falls by US$10 billion. The IS curve equation shows that, if the goods market is in equilibrium and the interest rate increases by one percentage point, output has to decrease by US$4 billion to maintain equilibrium. EconLit subject codes: E120, E200

3 FINDING THE IS CURVE 3 Finding the IS curve for a hypothetical economy The purpose of this paper is to illustrate in a model of a hypothetical economy how the equilibrium in the goods market is determined when both income and the interest rate are endogenous. I derive the equation describing equilibrium in the goods market (the IS schedule) using algebra. The structure of the goods market of a hypothetical economy given in Gordon (1998, p. 121, problem 1) is represented by the following equations: C = a (Y-T) (1) a = 50-10r (2) T = Y (3) I p = r (4) G = 400 (5) No units of measurement are given; I assume that C, Y, T, a, I p, and G are all measured in billions of US$. The interest rate r is measured in percent. The demand for domestic final product (Z) is: Z = C + I p + G + EX - IM (6) As no information is provided on exports (EX) or imports (IM), I assume the economy is closed and both exports and imports equal zero. Demand for domestic final product (planned expenditures) then reduces to: Z = C + I p + G (7) Substitute the given functions for C (equations 1 and 2), I p (equation 4) and G (equation 5) into equation 7, to obtain planned expenditures: Z = (50-10r) [Y - ( Y)] (8)

4 FINDING THE IS CURVE 4 Expanding and grouping terms in r and Y yields: Z = [50 - (0.75)(200) + 400] - 10r + [ (0.75)(0.2)]Y, or: Z = r Y Hence the planned expenditures equation is: Z = r Y (9) When income increases by US$1 billion, demand for domestic final product increases by US$0.60 billion. When the market interest rate increases by 1 percentage point, demand for domestic final product falls by US$10 billion. The IS-curve represents all combinations of income (Y) and interest rate (r) at which the goods is in equilibrium (Blanchard, 2006, p. 95). The goods market is in equilibrium when the supply of domestic final product (Y) equals demand for domestic final product (Z): Y = Z (10) Substitute the expression Z = r Y derived above for Z to rewrite the equilibrium condition as: Y = r Y (11) Solve for income (Y): Y Y = r, or 0.40Y = r, or Y = (1/0.40) (300-10r), or Y = 120-4r Hence the equation for the IS curve (see figure 1) is: Y = 120-4r (12)

5 FINDING THE IS CURVE 5 If in goods market equilibrium the interest rate increases by one percentage point, output has to decrease by US$4 billion to maintain equilibrium. Figure 1. IS curve (Y = 120 4r) representing equilibrium in the goods market

6 FINDING THE IS CURVE 6 References Blanchard, O. (2006). Macroeconomics (4 ed.). Upper Saddle River, NJ: Pearson th Prentice Hall. Gordon, R. J. (1998). Macroeconomics (6 ed.). Maddison, MA: Addison-Wesley. th