By studying, Will can produce a higher grade, Gw, on an upcoming economics exam.
ID: 1253465 • Letter: B
Question
By studying, Will can produce a higher grade, Gw, on an upcoming economics exam. His production function depends on the number of hours he studies marginal analysis problems, A, and the number of hours he studies supply and demand problems, R. Specifically, Gw = 2.5(A)^(0.36)B^(0.64). His roommate David's grade production function is Gd=2.5A^(0.25)B^(0.75).a. What is Will's marginal productivity from studying supply and demand problems? What is David's?
b. What is Will's marginal rate of technical substitution (MRTS) between studying the two types of problems? What is Davids?
c. Is it possible that Will and David have different marginal productivity functions but the same marginal rate of technical substitution functions? Explain.
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Explanation / Answer
a. Gw = 2.5(A)^(0.36)B^(0.64) Take the derivative with respect to B. Will's MPB =2.5*0.64*(A/B)^0.36 Will's MPB =1.6*(A/B)^0.36 Gd=2.5A^(0.25)B^(0.75) Take the derivative with respect to B. David's MPB = 2.5*0.75*(A/B)^0.25 David's MPB = 1.875*(A/B)^0.25 b. MRTS = MPA/MPB Gw = 2.5(A)^(0.36)B^(0.64) Take the derivative with respect to A. Will's MPA = 2.5*0.36*(B/A)^(0.64) Will's MPA = 0.9*(B/A)^(0.64) Will's MRTS = MPA/MPB Will's MRTS = 0.9*(B/A)^(0.64)/1.6*(A/B)^0.36 Will's MRTS = 0.9*(B/A)/1.6 Will's MRTS = (9/16)*(B/A) Gd=2.5A^(0.25)B^(0.75) Take the derivative with respect to A. David's MPA = 2.5*0.25*(B/A)^(0.75) David's MPA = 0.625*(B/A)^(0.75) David's MRTS = MPA/MPB David's MRTS = 0.625*(B/A)^(0.75)/1.875*(A/B)^0.25 David's MRTS = 0.625*(B/A)/1.875 David's MRTS = (1/3)*(B/A) c. Yes. All you need are different scalar multiples. For example, let's say Will had Gw = C*(A)^(p)B^(q) and David had Gd = D*(A)^(p)B^(q) where C does not equal D. They would have different marginal productivity function but the same MRTS.
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