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An individual has preferences for an aggregate consumption commodity (x) and health (H) represented by a...

An individual has preferences for an aggregate consumption commodity (x) and health (H) represented by a utility function U(x, H) = αln(x) + βln(H). The price of the aggregate commodity (x) is px and the price of medical care (m) is pm. The input of medical care (m) produces health (H) via a health production relationship that can be presented by the function g(m) = ln(m); that is H = ln(m).

a. Compute the optimal demand for medical care (m), the aggregate consumption commodity (x) and health (H) as functions of prices (px, pm), income (y), and the parameters of the model (α, β). You may assume a standard budget constraint.

b. Calculate the price elasticity of demand for medical care.

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