Intertemporal Choice Question Part 1

An agent lives for two periods. Her utility from consumption in period 1(c1) and consumption in period 2 (c2) is given by u(c1,c2) =log(c1) + b log(c2) , where b is the discount factor reflecting her time preference. The agent earns incomes w1 in period 1 and w2 in period 2. The rate of interest is r greater than 0 The agent chooses c1 and c2 so as to maximize u subject to her budget constraint. Consider a temporary increase in income where w1 increases but the agent does not change her expectations about w2 .Then the marginal propensity to consume of present consumption with respect to w1 (dc1 by dc2) is given by