Production Concepts
What is the difference between the short run and long run in production?
• Short run → at least one input is fixed
• Long run → all inputs are variable
• Time frame depends on industry, not calendar time
Given Q = 10L – 0.5L² + 24K – K², find MPL.
MPL=10–L
What is the difference between accounting and economic profit?
• Accounting profit = TR – explicit costs
• Economic profit = TR – (explicit + implicit costs)
• Opportunity costs included in economic profit
If TC = 270 + 30Q + 0.3Q², find MC.
MC=30+0.6Q
What is the Law of Diminishing Marginal Returns?
• As one input increases, output rises at a decreasing rate after a certain point
• Marginal product eventually declines
• Caused by overuse of a variable input relative to fixed inputs
If price = $40/unit and MPL=5, what is MRPL?
MRPL=40×5=$200
What are fixed and variable costs?
• Fixed costs don’t change with output (rent, insurance)
• Variable costs change with output (labor, materials)
• At zero output, TVC = 0 but TFC still exists
If TC = 270 + 30Q + 0.3Q², find AVC.
AVC=30+0.3Q
What is the profit-maximizing hiring rule for labor?
• Hire workers until MRPL = MCL
• If MRPL > MCL → hire more
• If MRPL < MCL → hire fewer
A firm’s production function is
Q = 60L - L^2
The output price is $2 per unit, and the wage is $16 per hour.
Using MRPL = MCL, find the profit-maximizing level of labor L*.
Find MPL = dQ/dL = 60 – 2L
MRPL = P × MPL = 2(60 – 2L)
Set MRPL = 16 and solve for L
L = 26*
What is the formula for ATC and how is it interpreted?
• ATC=AFC+AVCATC = AFC + AVCATC=AFC+AVC
• ATC=TC/QATC = TC/QATC=TC/Q
• Shows cost per unit of output
If TC = 270 + 30Q + 0.3Q², at what Q is ATC minimized?
Q=30
What does “returns to scale” mean?
• How output changes when all inputs change proportionally
• Increasing returns → output > input change
• Constant returns → output = input change
• Decreasing returns → output < input change
A firm has production function:
Q=4(K^1/2)(L^1/2)
Input prices: wage PL=$5, capital price PK=$20
Total budget for inputs is $100.
Using cost-minimizing input choice, how many labor hours (L) and machine hours (K) should the firm use?
Use condition MPL/PL=MPK/PK
For Q=4(K^1/2)(L^1/2):
MPL=2(K^1/2)(L^−1/2)
MPK=2(L^1/2)(K^−1/2)
Get relationship L = 4K
Use budget: 5L+20K=100⇒L=10,K=2.5
When MC > ATC, what happens to ATC?
• ATC is rising
• If MC < ATC → ATC falling
• If MC = ATC → ATC at minimum point
If TC = 270 + 30Q + 0.3Q², what is the ATC at its minimum?
ATC=48
For a Cobb-Douglas function Q=c(L^α)(K^β), what determines returns to scale?
• The sum α+β:
>1 = increasing
=1 = constant
<1 = decreasing
• Reflects how efficiently inputs combine at scale
A firm uses labor (L) and capital (K). Their productivities and prices are:
MPL=30 units per worker
MPK=60 units per machine
Wage PL=$15 per worker
Rental rate of capital PK=$40 per machine
Is the firm using its inputs efficiently? If not, which input should it use more of and which less?
Compute MPL/PL and MPK/PK
MPL/PL=2 units per dollar
MPK/PK=1.5 units per dollar
Labor is more productive per dollar → use more labor, less capital
What is the minimum efficient scale (MES)?
• Output level where LRAC is minimized
• Point where economies of scale are fully realized
• Beyond this, diseconomies may begin
If TC = 1000 + 174Q – 4Q² + Q³, find MC.
MC=174–8Q+3Q^2