代写EFIM10023 Mathematics for Economics代写Java编程

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One economist wants to understand the consumption of housing in the United Kingdom. She assumes that households have the following utility:

where ch denotes the consumption of housing and cn denotes the consumption of the rest (non-housing, hence n). We have also 0 < α < 1.

She would like to estimate ρ in the data; she is less interested in α.

1. Calculate the (log) marginal rate of substitution between housing and non-housing. as a function of the (log) relative consumption.

2. Intuitively, the marginal rate of substitution between housing and non-housing should relate to the relative price between housing and non-housing ph/pn. How, and why?

3. Assume that the economist observes the (different) relative expenditures (phch)/(pncn) and relative prices ph/pn faced by individuals surveyed all across the United Kingdom. How could she use the data to estimate the parameter ρ (using the previous questions)?