Even if we are willing to dispose of its main assumption1 namely that population growth responds positively to percapita oousuanyznvtion1 the Malthus model can still only reasonably explain persistent crosscountry diEerences in percapita outputfconsuniption via diEerences in land per capita.1 To the extent that land per capita is not a good empirical predictor of GDP-percapita, we must search for another explanation to account for the dierences in GDP that we observe empirically. The Solow model based on Solow [1956) and captured by equations (SH[Sal] does this by introducing physical capital. output: y: = 2k? {51} Consumption: a. = (1 _ 3m. [82} Investment: it = 53;! {83} Capital: em = {1 ink. +z'E {S4} where 2 denotes technology, a E [I], 1] is a timeinvariant savings rate out of current production1 d E [I], 1] is depreciation of capital1 and or E [I], 1} is a production parameter capturing the marginal productivity of capital. a} [2 points} Assuming i=0 2::- , per-capita capital converges to a unique steady state it\" in the Solow model. Combining equations [51}. [33}, and [34} while setting kt\" = is: = k\ization (s', 2") - what happens to consumption over time if technology suddenly increases from 2" to 2" > >"? What happens to consumption if the savings rate suddenly increases from s' to Sar > 5", where say is the golden rule savings rate? d) (4 points) Assuming technology is common across countries, can the basic Solow model (without technological advancement) explain temporary differences in cross-country output/consumption per capita? How about permanent ones? e) (2 points) Assuming technology is common across countries, can the full Solow model (with technological advancement) explain temporary differences in cross-country output/consumption per capita? How about permanent ones