Assume that production in an agricultural economy takes place according to Y = ATQ'ELn'B where Y is output. A is technology. T is the amount of land and L is the labour force. This means that growth in this economy can be decomposed as follows. gy = g" + 0.5911 + 0.5gL,where gy- is the growth rate of output, 9' is the growth rate of technology, 91- is the growth rate of land and 9;, is the growth rate of the labour force. Assume that everyone in this economy works and so the labour force is equal to the population, which grows at a rate 11 > 0. Assume that the quantity of land is xed. Answer all parts below: (a) Find an expression for the growth rate of per-capita income. (b) Using this equation, explain why the Malthusian Trap could be present in this economy. to) Why might the Malthusian Trap not apply in this economy? Carefully explain under what conditions the Matthusian Trap will and will not apply in this economy