Sara is a college student who receives from her parents a weekly rent of 100 and is considering working part-time to earn more. Sara’s preferences over consumption C and leisure L are described by the following utility function: U=C1/2L1/2 This utility function implies that her marginal rate of substition is MRS(L,C)=MUL/MUC=C/L The average price of the consumption goods and services that Sara normally buys is P=2 and the hourly wage that she can command is w=10. Considering the time Sara needs to devote to her studies, she can freely allocate about T=20 hours per week to either work or leisure activities. (a) Write down Sara’s budget constraint. Represent it graphically, indicate what is its slop and its vertical intercept and explain their economic meanings. (10 points) (b) Derive Sara’s optimal choice of consumption, leisure and labour supply. Represent the optimal choice on a graph. (9 points) (c) After some time and given the experience she has accumulated, Sara can command a higher wage of w=12.5. How does this change the budget constraint? Write down the expression of the new budget constraint and represent it graphically highlighting the differences with the old one. ( 8 points) (d) Derive the new optimal choice of Sara under the new budget constraint. ( 8 noints)
