A fitness company offers online classes (x) for $10 per class. The typical customer has monthly utility from online fitness classes (x) and money spent on other things (m) U(x,m) = m + 40x0.5 and a monthly budget of $200.

a) Compute the expression of the Marginal Rate of Substitution of money for on-line classes. Does it depend on how much money the consumer spends on other things? Does the typical customer consider on-line classes an imperfect substitute to spending money on other things?

b) Find the weekly optimal bundle of the typical customer. Keep in mind that the unit price of money spent on other things is $1.

c) What is the typical customer's level of utility at the optimal bundle?

Suppose that, due to an economic downturn, the monthly budget of the typical customer declines to $100.

d) What happens to the number of online classes the typical customer follows each week?

e) Illustrate this result in an indifference curve diagram where you measure online classes along the horizontal axis and money spent on other things along the vertical axis.

Suppose the economic crisis is over and the typical customer's budget is back to $200 per month when the fitness company decides to introduce a new price menu. Now, customers must pay a monthly fee of $40 but then they can buy online classes for $5 each only.

f) Under what pricing scheme does the typical customer spend more money on online classes?

g) Under what pricing scheme does the typical customer take more online classes?

h) Does the new pricing scheme make the typical customer better off, worse off, or just the same?