this question please!!

2. Kate earns an income of $500 from her iob as a waitress at The Crusty Cantab and receives an additional $100 from her grandmother to help her manage. She spends all of her total income either on hours of education or on crabbie patties. The market price for an hour of education (Poo) is $10fhr, while the price of crabbie patties (PPalty:l is $10 f patty [organic all the way!]. initially. Kate maximises utility by consuming 50 hours of education and 10 patties. Assuming Kate has standard [bowed in toward the origin) indifference curves reecting her preferences for education and patties. draw a well-labeled diagram showing this optimum. [Put hours of education on the iii-axis] Label the intercepts and slope ofthe budget constraint as well as her optimum consumption point. What is her MRS out of patties and into education at this optimum? Why? A new government program provides a subsidy for education to certain members of the labor force. Kate qualifies for a subsidy that effectively reduces her hourly education costs to $8 I hour. She now optimizes by consuming 12 crabbie patties. What happens to her optimal hours oi'education? Be specific (namely. give the new number of hours of education she consumes after the subsidy]. Show this new optimum situation on your graph from {a}. Label any new relevant intercepts and slopes. Grandma learns ofKate's subsidy benefit and decides she no longer needs the $100 gift. Grandma thus takes it back. Can Kate still afford the optimum she chose in part [3]? Why or why not? Where will she maximize utility now? [Hint you cannot give exact answers here but you CAN tell us where she will consume relative to her optimum in [a]]. Again. show this optimum on the graph you've used in [a] and [b]. Again, he sure to label any new intercepts and slopes. [Noter Kate's hourly education costs remain at $0 Z hour.]