Jeff Bezos is opening a Amazon fulfillment center in South Park, Colorado, and employs Stephen Stotch...
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Jeff Bezos is opening a Amazon fulfillment center in South Park, Colorado, and employs Stephen Stotch for q hours a day for a wage of p. Jeff's profits are = V(q)- p, where V(g), is increasing and concave. Stephen's utility is u = p-cq, where ce [ce] has distribution G(c) and density g(c). His outside option is 0. Help Jeff maximize profits by proposing mechanism (p(c), q(c)), where è is Stephen's self-reported cost type. a) Write down Stephen's utility, u(c, c), given his true cost c and his report c. Show that in a truthful (i.e. "incentive compatible") mechanism, utility U(c) = u(c, c) is given by U(c) = f*g(s)ds + U(e) b) Show that Stephen's ex-ante expected utility is [*U(e)dG(e) = [ {q(e)G(e)] de + U(e) c) Show that in Jeff's optimal mechanism, profits equals where T= - [* [V (q(e)) – MC (c)q(e)}dG(e) G(c) g(c) What is the optimal number of hours worked, q* (c)? d) Suppose V (q) = log(q) and c~ U[0, 1]. What is q (e)? What is the efficient quantity? MC(c) = c + Jeff Bezos is opening a Amazon fulfillment center in South Park, Colorado, and employs Stephen Stotch for q hours a day for a wage of p. Jeff's profits are = V(q)- p, where V(g), is increasing and concave. Stephen's utility is u = p-cq, where ce [ce] has distribution G(c) and density g(c). His outside option is 0. Help Jeff maximize profits by proposing mechanism (p(c), q(c)), where è is Stephen's self-reported cost type. a) Write down Stephen's utility, u(c, c), given his true cost c and his report c. Show that in a truthful (i.e. "incentive compatible") mechanism, utility U(c) = u(c, c) is given by U(c) = f*g(s)ds + U(e) b) Show that Stephen's ex-ante expected utility is [*U(e)dG(e) = [ {q(e)G(e)] de + U(e) c) Show that in Jeff's optimal mechanism, profits equals where T= - [* [V (q(e)) – MC (c)q(e)}dG(e) G(c) g(c) What is the optimal number of hours worked, q* (c)? d) Suppose V (q) = log(q) and c~ U[0, 1]. What is q (e)? What is the efficient quantity? MC(c) = c +
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To maximize profits we need to find the optimal mechanism for Jeff Bezos in this scenario Lets go through the steps a Stephens utility uc c given his ... View the full answer
Related Book For
Statistics for Business and Economics
ISBN: 978-0321826237
12th edition
Authors: James T. McClave, P. George Benson, Terry T Sincich
Posted Date:
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