Question about Dixit-Stiglitz model of monopolistic competition:

Consider a Dixit-Stiglitz model of monopolistic competition. There are N monopolistic producers of intermediate goods. q... using the labour and capital. a. = nklilp" (2) where 9,. :> 0 and 1 > 0. Final goods producers operate using the following production function. 1 1 F Y = [Nap ((91)p+(f12)P + - - . + (q~)')] (3) where p E (0. l). (a) Given a nal good price P. derive and interpret the 'Marshallian demand' for each good :1\". (b) Use your answer in part (a) to derive and interpret the equilibrium price of an intermediate good as a function of p and the unit cost 0,1,. (c) Equilibrium prots of each intermediate good rm can be written as 1131/ 9 \"'1 =__ is 4 1' 0N(3) H where o = , is the elasticity of substitution between intemiediate goods. Provide a clear interpretation of each element of the prots accruing to individual intermediate good producers. ((1) Explain how equation (4) may be tinn-varying.i.e..1rn(t). How does the expected future path of in, (t) relate to the present valuation of a rm