Question

Start with the demand side. The household in question has the following Cobb- Douglas utility function: The household also faces the following budget constraint: The above says that the household's after-tax income, (1-T)Y, is divided between consumption of goods and services, C,, and the amount spent on housing services (r+0+ τ.)P,HH, . This latter variable can be thought of as the user cost of housing and consist of the rate of interest (r), the rate of depreciation (6) and residential 4 taxes (Tz). Saving is zero and you can think of this as representing a young household with no assets th debt. at finances the purchase of the house with 100 per cent

Answer 1

Given That: Start with the demand side. The household in question has the following Dougkas cetility Function. = > Maximize the utility Function subject to the given constraint L = H^n_t c_t^1 - n = lambda(1 - T)y_t - c_t - (r + delta + TR) P^H_t H_t dt/dH = n H^n - 1_t + lambda (r + delta + T_R) P^H_t = 0 dt/dl = (1 - n) c^-n_t H^n_t + lambda = 0 dL/d lambda = (1 - T)y_t - c_t - (r + delta + TR) p^H_t H_t = 0 using the equations dL/dH and dL/dc we get eta 1 + t^eta - 1 c^1 - eta_t = -lambda (r + delta + T_R) P^H_t (1 - eta) C^-n_t = -lambda using the above equations we get relation between it and c. \r\n eta lt^n - 1_t = H^n_t (1 - eta) C^n_t (r + delta + T_R) p^H_T H_t = eta/(r + delta + T_R)p^H_t c_t