Economics 2150A/B Lecture 8: Chapter 8 – Cost Curves
22 Jun 2018
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Chapter 8 – Cost Curves
Chapter 8 Overview
Introduction
Long-Run Cost Functions
oShifts
oLong-run average and marginal cost functions
oEconomies of Scale
oDeadweight loss – “A Perfectly Competitive Market Without Intervention Maximizes Total
Surplus”
Short-Run Cost Functions
The Relationship Between Long-Run and Short-Run Cost Functions
Long-Run Cost Functions
Definition – The long run total cost function relates minimized total
cost to output, Q, and to the factor prices (w & r)
oTotal Costs (TC): TC (Q, w, r) = wL*(Q, w, r) + rK*(Q, w, r)
oL* & K* are the long-run input demand functions
As Quantity of Output increases from 1 million to 2 million, with
input prices (w, r) constant, cost minimizing input combination
moves from TC1 to TC2 which gives the TC(Q) curve
Example – What is the long-run total cost function for production
function Q = 50L1/2K1/2
oFollowing equation describe the cost-minimizing quantities of labor and capital:
L=(Q/50) √(r/w) & K=(Q/50) √(w/r)
oTo find the minimized total cost, we calculate the total cost the firm incurs when it uses this
cost-minimizing input combination:
TC(Q) = wL+rK = (w)Q/50 √(r/w)+(r)Q/50 √(r/w)=2 √wr/50 Q
oWhat is the graph of the total cost curve when w = 25 and r
= 100?
TC(Q) = 2Q
Tracking Movement
oDefinition: The long run total cost curve shows minimized
total cost as output varies, holding input prices constant
oGraphically, what does the total cost curve look like if Q varies and w & r are fixed?
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Identifying Shifts
oGraphically, how does the total cost curve shift if
wages rise but the price of capital remains fixed?
Change in input prices
oPrice of input increases proportionately by 10%.
Cost minimization input stays same, slope of
isoquant is unchanged TC-curve shifts up by 10%
Long-Run Average Cost Function (LRAC Function)
Definition – The long run average cost function is the long run total cost function divided by output, Q.
oTells us the firm’s cost per unit of output AC (Q, w, r) = TC(Q, w, r)/Q
Long-Run Marginal Cost Function
oDefinition – The long run marginal cost function measures the rate of change of total cost as
output varies, holding constant prices
MC (Q, w, r) = {TC (Q + ∆Q, w, r) – TC (Q, w, r)}/∆Q = ∆TC (Q, w, r)/∆Q
Where: w & r are constant
Relationship between Average & Marginal Cost Curves
oSuppose that w & r are fixed:
When marginal cost is less than average cost,
average cost is decreasing in quantity. That is, if
MC (Q) < AC (Q) AC (Q) will decrease in Q
When marginal cost is greater than average cost,
average cost is increasing in quantity. That is, if MC
(Q) > AC (Q) AC (Q) will increase in Q
When marginal cost equals average cost, average
cost does not change with quantity. That is, if MC
(Q) = AC (Q) AC (Q) is flat with respect to Q
Economies & Diseconomies of Scale
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ECON 2150A/B Full Course Notes
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Document Summary
Long-run cost functions: shifts, long-run average and marginal cost functions, economies of scale, deadweight loss a perfectly competitive market without intervention maximizes total. The relationship between long-run and short-run cost functions. As quantity of output increases from 1 million to 2 million, with input prices (w, r) constant, cost minimizing input combination moves from tc1 to tc2 which gives the tc(q) curve. Example what is the long-run total cost function for production function q = 50l1/2k1/2: following equation describe the cost-minimizing quantities of labor and capital: K=(q/50) (w/r: to find the minimized total cost, we calculate the total cost the firm incurs when it uses this cost-minimizing input combination: Tc(q) = wl+rk = (w)q/50 (r/w)+(r)q/50 (r/w)=2 wr/50 q: what is the graph of the total cost curve when w = 25 and r. Change in input prices: price of input increases proportionately by 10%. Cost minimization input stays same, slope of isoquant is unchanged tc-curve shifts up by 10%
