Chapter 9: Input Use and Demand for Inputs
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Chapter 9:
Input Use and Demand for Inputs
Key Topics
1. Derived demand for inputs
2. Revenue concepts related to input usea. Total revenue product (TRP)
b. Average revenue product (ARP)
c. Marginal revenue product (MRP)
3. Profit-maximizing input levela. Profit-max input rule (MRP = input P)
b. Input demand curve
c. Shifts in factor demand curves
Derived Demand
The demand for resources (inputs) is dependent on (or derived from) the demand for the outputs those resources can be used to produce.
Input & Output Decisions
Related via production function
q
q*
L* L
TP
Q* = profit-maximizing q L* = profit-maximizing L
Revenue Concepts that are functions of input usage
Total Revenue Product (TRP)Average Revenue Product (ARP)Marginal Revenue Product (MRP)
Revenue Products
Total Revenue Product
= TRP
= TP x P
= paired observations on the $ value of output and physical units of a variable input
Revenue Products
Average Revenue Product
= ARP
= AP x P
= revenue per unit of input
Revenue Products
Marginal Revenue Product
= MRP
= MP x P (= MR*)
= additional revenue per unit of additional input
*for competitive firm
Total RevenueProduct ($)
Average &Marginal RevenueProduct ($)
TP x P = TRP
AP x P = ARP
Input a
MP x MR = MRP
Input a
0
0
A
B C
a1 a2 a3
a1 a2 a3
Profit-Maximizing Input Level
Keep using an input up to the point where the additional revenue from the last additional unit equals the additional cost
MRP = input P
Labor Price (= w)
$
P
S
DL
$
L
MktFirm
P = w
Profit-Maximizing Input Level
$
$
LL*
TRP
TCπ*L*
LMRP
wARP
Find D for Variable Input (e.g. L)
$
ARP
W3
W2
W1
MRP
LL3 L2 L1
Increased D for Labor (examples)
$
w
w1
w2
MRP
LL1 L2
Increased D for Labor (examples)
$
P ofOutput
LL1 L2
w P2 > P1
MRP2 (P2)
MRP1 (P1)
Increased D for Labor (examples)
$
MP
MP2 > MP1
w
L
MRP2 (MP2)
MRP1 (MP1)
L1 L2
Profit-Max Input Rule = Profit-Max Output Rule
MRP = MFC MPL ∙ MR = w
MR = w / MPL
MR = MC
Profit Max Input Side = Profit Max Output Side
TPq
q*
LL*
Profit Max Input Side = Profit Max Output Side
$
w
MRP
LL*
Profit Max Input Side = Profit Max Output Side
$
MC
MR
qq*
Other Input Economics Applications
1. Professional athletes (salaries)
2. Land (rent and usage)
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