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ECO310_Fall2008_Final_SectionB_solutions

# ECO310_Fall2008_Final_SectionB_solutions - ECO 310...

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ECO 310 – Microeconomic Theory: A Mathematical Approach Spring 2008 Solutions to the Final Examination Section B Question 4 (i.a) The cost of producing Q units is minimized by setting 10 K = L = Q so LRTC ( Q ) = r ( Q/ 10)+ wQ , LRAC ( Q ) = LRTC ( Q ) /Q = r/ 10+ w and LRMC ( Q ) = dLRTC ( Q ) /dQ = r/ 10 + w . (i.b) When K = 10 we have Q = min(100 ,L ) hence production is limited to a maximum of 100 units. For Q 100 we have SRTC ( Q ) = 10 r + wQ , SRAC ( Q ) = 10 r/Q + w and SRMC ( Q ) = w . (ii.a) When Q = K + L we will only use the cheapest input. Therefore LRTC ( Q ) = ± rQ, if r w wQ, otherwise LRAC ( Q ) = ± r, if r w w, otherwise LRMC ( Q ) = ± r, if r w w, otherwise. (ii.b) When K = 10 we have Q = 10 + L . Therefore for Q 10 we have SRTC ( Q ) = 10 r + w ( Q - 10), SRAC ( Q ) = 10 r/Q + w ( Q - 10) /Q and SRMC ( Q ) = w . Question 5 (i) Denote by p ( x ) the equilibrium price for each x [0 , 50]. In equilib- rium all books must be sold. The condition for all books to be supplied

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ECO310_Fall2008_Final_SectionB_solutions - ECO 310...

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