Jon is studying for an exam. There are two "inputs" to the grade he

receives: hours per week spent working on problem sets (S) and hours per week

reviewing lecture videos V . Through trial and error, he has deduced that the

grade q [0, 100] that he receives on his exams is approximately given by

q(S, V ) = 10 S^3/4 V^1/4

a) Sketch an isoquant for Jon with S on the x-axis and V on the y-axis,

and write the expression for his marginal rate of technical substitution (MRTS).

Interpret its value when S = V .

b) Suppose that the effort "cost" for Jon to watch lecture videos V is

r_V = $5. What cost r_S of problem set hours leads Jon to spend twice as

many hours solving problem sets as watching lecture videos?

c) Suppose that r_S = $15 and r_V = $5. Derive and draw the expansion path

for Jon. How much will it "cost" Jon to get a grade of q?

d) As Jon is studying, the unthinkable happens: his internet connection

is lost! He still has access to the problem sets (which he downloaded in advance),

but he cannot access the lecture videos. Derive his short run cost function C(q)

given that his total time spent watching the video lectures is "stuck" at V (V bar) = 16.

(Hint: use the production function to determine how much S he needs to achieve

a grade of q.)

e) Jon's parents have agreed to pay him $1.50) for every point he

receives on the test, so he will receive $1.50q if he gets q points on the test.

Unfortunately, his internet connection is still down, and the Comcast can't fix

the issue until after the test is due. What grade will Jon receive?