Question: 1. Consider the following utility function and corresponding marginal rate of substitution for consumption, C and leisure, and L: U = CL square ( just the L is square, the C is normal) and MRS = - L/2C . The consumer's income is $100, PL = 20, and PC = 10.
(a) Define the budget line and illustrate in a graph (L is on the Y axis).
(b) Find the marginal rate of transformation.
(c) Define the 2 equations needed to calculate optimal utility.
(d) What is the optimal consumption bundle? Does this make sense?
(e) How much utility does this consumer get?
2. Now, imagine the price of leisure drops from $20 to $16.67.
(a) Define the new budget line and illustrate in a graph (L is on the Y axis). (4 points) (b) Find the marginal rate of transformation.
(c) Define the 2 equations needed to calculate optimal utility.
(d) What is the optimal consumption bundle? Does this make sense?
(e) How much utility does this consumer get? Does this make sense?
(f) Graph the budget lines from 1a) and 2a) on the same graph.
(g) Calculate Total Effect.
(h) Calculate Substitution Effect.
(i) Calculate Income Effect.
3. Derive demand for both consumption and leisure.
4. Find the wealth expansion path.