A: We can then model exam grades as emerging from a production process that takes hours of
Question:
(a) On a graph with hours of sleep on the horizontal axis and hours of studying on the vertical, illustrate an isoquant that represents a particular exam performance level xA.
(b) Suppose you are always willing to pay $5 to get back an hour of sleep and $20 to get back an hour of studying. Illustrate on your graph the least cost way to get to the exam grade xA.
(c) Since the production process is homothetic, where in your graph are the cost minimizing ways to get to the other exam grade isoquants?
(d) Using your answer to (c), can you graph a vertical slice of the production frontier that contains all the cost minimizing sleep/study input bundles?
(e) Suppose you are willing to pay $p for every additional point on your exam. Can you illustrate on your graph from (d) the slice of the “isoprofit” that gives you your optimal exam grade? Is this necessarily the same as the exam grade xA from your previous graph?
What would change if you placed a higher value on each exam point?
(f) Suppose a new caffeine/Gingseng drink comes on the market — and you find it makes you twice as productive when you study. What in your graphs will change?
Suppose that the production technology described in part A can be captured by the production function x = 40ℓ0.25 s0.25 — where x is your exam grade, ℓ is the number of hours spent studying and s is the number of hours spent sleeping.
B: Suppose that the production technology described in part A can be captured by the production function x = 40ℓ0.25s0.25 — where x is your exam grade, ℓ is the number of hours spent studying and s is the number of hours spent sleeping.
(a) Assume again that you’d be willing to pay $5 to get back an hour of sleep and $20 to get back an hour of studying. If you value each exam point at p, what is your optimal “production plan”?
(b) Can you arrive at the same answer using the Cobb-Douglas cost function (given in problem 12.4)?
(c) What is your optimal production plan when you value each exam point at $2?
(d) How much would you have to value each exam point in order for you to put in the effort and sleep to get a 100 on the exam.
(e) What happens to your optimal production plan as the value you place on each exam point increases?
(f) What changes if the caffeine/Gingseng drink described in A(g) is factored into the problem?
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Step by Step Answer:
A a This is illustrated in panel a of Graph 1214 where x A represents the isoquant with all the input bundles that can produce exam grade x A b This is illustrated in panel a of the graph with the add...View the full answer
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Related Book For 
Microeconomics An Intuitive Approach with Calculus
ISBN: 978-0538453257
1st edition
Authors: Thomas Nechyba
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