Entrepreneurs in Wakanda, a country in a very remote region of the world discover many new technologies that together raises the productivity of the country in a phenomenal way. The productivity factor of the economy, AG, indeed increases by five fold. Assume that the economy can be described by a centralised representa- tive agent macroeconomic model, and that the baseline model produces the following outcomes or equilibrium solutions: consumption, c = 0.737 leisure, x = 0.6 labour, l = 0.4 utility, u = 0.56058 If the economy can still be characterised by the utility and production func- tions: u(c, x) = lnc + lnx y = AGl, TimeendowmentasT =l+x=1 and the parameters of the utility and production functions are calibrated just like the baseline model with the only exception being the increase in productivity factor from 1 to 5,

Page 2 Again, assume, the parameters of the the utility and production functions can be calibrated as follows: Productivity factor, AG= 5 Labour elasticity, = 13 Degree to which the agent prefers leisure to work, = 0.5 Time endowment, T = 1 Find: the new equilibrium values for and indicate what the value repre- sent. (a) Labour, l. [10 Marks] (b) Consumption, c. [10 Marks]. (c) Utility, u. [10 Marks] (d) Graph the equilibrium in a (c : l) space [10 Marks] ((f) Estimate the growth in output in the economy as result of the improve- ment in productivity.