The firm chooses how many units of the production input, ns, to purchase upfront from its supplier and how many units ni it wishes to contract for delivery from the intermediary that will arrive only in the event that the supplier cannot fully deliver the ns units of inputs. The firm borrows from the bank to pay for the cost pns + qn1. Nature reveals whether the supplier fully delivers ns. If so, production occurs, output is sold and the bank is repaid principal and interest, (1 + r)b. Otherwise, the qunplior dolivorg dn unita inputa the intormodiony dolivorg n. innuta

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Construct all the relevant partial derivatives of the Lagrangean and set each of these partial derivatives equal to zero.

The firm chooses how many units of the production input, n,, to purchase upfront
from its supplier and how many units nj it wishes to contract for delivery from
the intermediary that will arrive only in the event that the supplier cannot fully
deliver the ns units of inputs. The firm borrows from the bank to pay for the cost
pns + qni.
Nature reveals whether the supplier fully delivers ng. If so, production occurs,
output is sold and the bank is repaid principal and interest, (1+ r)b. Otherwise,
the supplier delivers øn, units of inputs, the intermediary delivers n¡ units of inputs,
production occurs, the firm pays the intermediary pini for delivery of the n¡ inputs
and the bank is repaid principal and interest, (1+ r)b
Transcribed Image Text:The firm chooses how many units of the production input, n,, to purchase upfront from its supplier and how many units nj it wishes to contract for delivery from the intermediary that will arrive only in the event that the supplier cannot fully deliver the ns units of inputs. The firm borrows from the bank to pay for the cost pns + qni. Nature reveals whether the supplier fully delivers ng. If so, production occurs, output is sold and the bank is repaid principal and interest, (1+ r)b. Otherwise, the supplier delivers øn, units of inputs, the intermediary delivers n¡ units of inputs, production occurs, the firm pays the intermediary pini for delivery of the n¡ inputs and the bank is repaid principal and interest, (1+ r)b
The problem of the firm can then be written as
max {T [f(ns) – (1+r)b,] + (1 – 1) [f(øns + n1) – prn1 – (1+ r)b.]}
-
-
Ns,n1,bs
subject to the constraint
PsNs + qn1 = b.
Transcribed Image Text:The problem of the firm can then be written as max {T [f(ns) – (1+r)b,] + (1 – 1) [f(øns + n1) – prn1 – (1+ r)b.]} - - Ns,n1,bs subject to the constraint PsNs + qn1 = b.
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