APPENDIX CHAPTER 11 FUNCTIONS AND GROWTH RATES

Y = F (K,L,T) This chapter uses mathematical notations to describe the relationship between output (Y) and labor (L) and capital (K) inputs: Y = F (K,L,T)(1) The amount of output the economy produces (Y) depends on how much capital (K) and labor (L) the economy has at its disposal and on the state of its technology (T).

Y = F (K,L,T) – cont. If we have more L and K, we expect more output; if technology improves, output will increase. The chapter uses dots above variables to denote annual rates of growth. A growth rate measures the rate at which something changes.

Y = ƒ(K,L,T) Production function Y = F (K,L,T) in terms of growth rate: Y = ƒ(K,L,T) Use this equation to calculate sources of economic growth.

Y = ƒ(K,L,T) - cont We can measure K and L but we cannot directly measure Ṫ, but we can calculate it as a residual. We use L’s share of income a 67 percent and K’s share of income as 33 percent. Express the growth rate equation as: Y = 0.67L K +T. (2)

Y - L = 0.67L K +T - L = 0.33(K – L) + T Growth per capita output, where per capita output is Y/P, P stands for population. In the long run, P and L grow at about the same rate = calculate it as the growth of Y/L. The growth rate of Y/L equals the growth rate of Y(Y) minus the growth rate of L(L).

Y - L = 0.67L K +T - L = 0.33(K – L) + T - cont If Y and L grow at the same rate, then Y/L will not change, if Y grows faster than L will Y/L grow. Calculate the growth rate of Y/L by subtracting L from each side of (2): Y - L = 0.67L K +T - L = 0.33(K – L) + T This is the equation for calculating the sources of per capita GDP growth.