Roots of economic development [21 marks] 4. Swee & Panza (2016) use historical data to identify the effect of good geography (location) on the formation of institutions. (i) To empirically identify the effects of location is particularly challenging because it is impossible to find exogenous changes in location ie. they are fixed. In this regard, could the availability of panel data that permits us to account for colony fixed effects help? Why/why not? What is the solution proposed by Swee & Panza (2016)? Explain. [3 marks] Consider a modification of the theoretical model in Swee & Panza (2016). A rent-extracting coloniser manages resource (i = R) and entrepot (i = E) colonies. There are three production inputs- labour , human capital hy, and judicial capacity jr - such that output y; = hil,"; where a governs the relative importance of human capital. Entrepot colonies are more reliant on human capital, so ap > ap- All output is valued at the same price p. The coloniser chooses investments in hi and ju and extracts a share t e (0,1) of the output. The native population chooses l, and retains 1 -t of the output. Assume convex costs for each input where cr (h, ) = #q() = $ and q00 = 4 (ii) For a given colony i, derive a mathematical expression for the optimal ratio of human capital to labour, h;/1;- [3 marks] (iii) Provide an intuitive interpretation for the expression that you have derived above. [2 marks]