A consumer's utility function is: U(c1, C2) = C1C2 where c, and c2 denote the planned consumption of composite good in period 1 and period 2, respectively. The consumption is on composite good and is...

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Extracted text: A consumer's utility function is: U(c1, C2) = C1C2 where c, and c2 denote the planned consumption of composite good in period 1 and period 2, respectively. The consumption is on composite good and is expressed in rupees. Suppose there is no inflation, so the prices of the composite good in each period are constant at 1 rupee. 1 The amount of money (income or endowment) the consumer will have in each period is denoted by m1 and m2. The consumer can borrow or save (lend) money at some interest rate r. (a) Write the consumer's utility maximization problem. Define the Lagrangian function for this utility maximization problem. Write the first order necessary conditions. (b) Find the optimal choice of composite good for each period as function of endowments and interest rate. 0.1. Find the optimal choice of composite good (c) Assume: m1 for each period (note that it is in rupees). Compute the saving in period 1. 200, т2 3D 100, and r = (d) Suppose interest rate rises to r = 0.2. Find the optimal choice of composite good for each period. Compute the saving in period 1. (e) Draw a graph showing the effect of increase in the interest rate on saving (draw just two points: saving at r = 0.1 and r 0.2).