Reference no: EM132592985

Peter 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 3/4V 1/4

a) Sketch an isoquant for Peter 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 Peter to watch lecture videos V is rV = $5. What cost rS of problem set hours leads Peter to spend twice as many hours solving problem sets as watching lecture videos?

c) Suppose that rS = $15 and rV = $5. Derive and draw the expansion path for Peter. How much will it "cost" Peter to get a grade of q?

d) As Peter 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 ¯ = 16. (Hint: use the production function to determine how much S he needs to achieve a grade of q.)

e) Peter'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 Peter receive?