Please solve these questions, thx!

6. Land in the Solow Growth Model (35 points total) Consider the following Solow growth model which features three factors of production: capital (Ht), labor (Ht), and land (Lt). The model consists of the following equations: Production function: Yt = HtaNtLtla (Note: both {I and {I} are strictly,F between t) and 1 i.e., I} s: {I s: 1 and {1 s: (I) s: 1 ). Capital accumulation: Kt+l = Hail _ 5) + It Investment: ft = St = SF: Labor supply: m==1 Supply: of Land: n=E (Note: E is not 1}. a.) (5 points) Substitute these equations to get a single equation describing Kt+1 in terms of Kr and the parameters (1.\c.) (6 points) Solve for the steady state capital stock (K*) in terms of the parameters a, o, 6, s and L . d.) (6 points) Use the production function to find an expression for the marginal product of land (MPL,). Write the MPL, in terms of the ratio and parameters a and o. e.) (6 points) The price pr of a unit of land at time t satisfies the following equation: pt 1 1+r [MPL+ +1 + Piti] where r is a constant steady state real interest rate. Assume that the marginal product MPL, is constant in the steady state at MPL = m, solve for the price of land in the steady state. Your answer should be in terms of m and r. Hints: Write p, as an infinite summation and then use the trick for the sum of an infinite geometric series .f.) (15 points) Use your answers to part (c) and (d) to solve for the ratio of the total Tralue of 11%: land (pg'i) relative to GDP (Yr). That is= nd an expression for . Your answer should Vt be in terms of the parameters (1, (I) and T