Consider the following consumption-leisure model, which is augmented to include a demand for money. A representative consumer has the utility function defined over consumption () and leisure () given by: (, ) = ln() + ln() where , (0,1) and + = 1. The consumer values leisure but, in order to consume, must spend time shopping (), which reduces the time available for leisure. The time constraint is given by + = , where is a fixed parameter. Shopping time depends on the desired level of consumption, as well as real money holdings (). It is assumed that holding more money reduces shopping time. Let = 2 ( 1 2 1 2). Lastly, assume that real money holdings responds to the real interest rate () as follows: = 0 + 1, where 0, 1 > 0. (a) Derive an expression for the optimal level of consumption as a function of leisure and the parameters of the model. (b) How does consumption change as the interest rate changes? Explain your answer.