1. Consider the constrained optimisation problem where an individual is deciding the optimal combination of two goods to consume. In this question, consider the example of an individual who is deciding which combination of free time and grade they expect to receive.

1. Explain why we might expect a production function to be concave. What does this imply for marginal productivity? Explain what this means in the context of additional hours of free time and additional hours of study. (5 points)

1. How do the Marginal Rate of Substitution (MRS) and the Marginal Rate of Transformation (MRT) help find the optimal choice of free time and study hours? What do the MRS and MRT represent in this context? (5 points)

1. Draw the equilibrium for an individual who chooses to get a grade of 75 and who studies for 9 hours per day. Draw the feasible frontier, the indifference curve, the optimal allocation and show where the MRS and MRT can be seen on the curves. (5 points)

1. What would happen to the equilibrium if the student's flatmates temporarily moved out of the shared accommodation, which meant the value of free time has now reduced? (Hint: this doesn't affect what's feasible, but what's preferred.) (5 points)