ECO 220 Exam 2

Short run

At least one input is fixed

Long run

All inputs can be adjusted

Marginal Product

𝑀𝑃𝐿 = 𝛥𝑞/𝛥𝐿, holding 𝐾 fixed
𝑀𝑃𝐾 = 𝛥𝑞/𝛥𝐾 with 𝐿 fixed

Marginal product measures additional output from additional input.

Average product

𝐴𝑃𝐿 = 𝑞/𝐿
𝐴𝑃𝐾 = 𝑞/𝐾

Average product measures output per unit of input. for a change involving several input units, 𝛥𝑞/𝛥L is the average incremental product over that interval.

Diminishing Marginal Product

Adding more of one input while holding other inputs fied eventually reduces its marginal product.

Does not mean total output is falling, output still rises while marginal product remains positive

If MP exceed AP, AP rises; if MP is below AP, AP falls.

MP crosses AP and AP’s maximum

Isoquants

An isoquant contains input combinations that produce the same output.

Isoquant slope: −𝑀𝑅𝑇𝑆𝐿𝐾

For small changes along an isoquant: 𝛥𝐾/𝛥𝐿 ≈ −𝑀𝑅𝑇𝑆LK

Marginal Rate of Technical Substitution (MRTS)

𝑀𝑅𝑇𝑆𝐿𝐾 = 𝑀𝑃𝐿 /𝑀𝑃𝐾
MRTSLK measures how many units of capital can be given up for one more unit of labor while maintaining output. The marginal-product ratio gives the local tradeoff; a large finite change need not have the same ratio throughout.

Technology Patterns

Standard convex:

• Property: Bowed toward the origin; diminishing MRTS as L rises along an isoquant

• How to Recognize: replacing capital with labor becomes progessively harder

Perfect Substitutes:

• Property: Straight isoquants, constant MRTS

• How to Recognize: Inputs replace one another at a constant rate

Perfect Complements:

• Property: L-shaped isoquants

• How to recognize: Inputs are needed in fixed proportions; extra input alone may add no outuput

Homothetic:

• Property: MRTS depends only on K/L

• How to recognize: the slope is the same along a ray from the origin

Quasilinear:

• Property: MRTS depends on the amount of only one input

• How to recognize: isoquants have a parallel-shift structure in one direction

Returns to Scale

How output changes when all inputs increase by the same proportion. This is a long-run concept.

Compare f(λK, λL) with λf(K, L), for λ > 1: greater means increasing returns; equal means constant returns; smaller
means decreasing returns.

Types of returns to scale

Increasing returns to scale (IRTS): Doubling all inputs more than doubles output

Constant returns to scale (CRTS): doubling all inputs exactly doubles output

Decreasing returns to scale (DRTS): doubling all inputs less than doubles output

Diminishing Marginal Product vs Returns to scale

Diminishing marginal product: concerns increasing one input while holding others fixed

Returns to scale: concerns increasing all inputs proportionally

Isocost curves

All combinations of inputs (e.g., labor and capital) that cost C dollars. There exists an isocost curve for every possible cost (infinite possible curves)

𝐶 = 𝑤𝐿 + 𝑟𝐾
w = wage per unit of labor

r = rental price per capital unit

Interior Solution

𝑀𝑅𝑇𝑆𝐿𝐾 = 𝑀𝑃𝐿 /𝑀𝑃𝐾 = 𝑤/𝑟

Find the lowest isocost that reaches the target isoquant. for smooth convex isoquants with both inputs used, the curves are tangent

MRTSLK describes the technology’s ability to substitute inputs; w/r describes the market opportunity cost of labor in units of capital.

Changes in input prices

With substitutable inputs, a higher wage generally encourages a least-cost mix with less labor relative to capital for a fixed output. The adjustment can be limited or absent for fixed-proportion technology or a fixed input. A higher input price cannot lower the minimum cost of producing an unchanged target, holding technology fixed

Expanding output in the short run and long run

Cost functions

Economic profit = total revune - explicit costs - implicit costs.

Cost Classifications

Variable Cost: changes with output as variable input use changes. There are variable costs sin the short and long run.

Fixed cost: does not vary with output over the relevant period; connected to fixed inputs. There are no fixed in the long run. In the standard short run model, fixed coasts are paid even at q = 0.

Avoidable Costs: can be avoided by changing the decision under consideration

Sunk costs: an expenditure incurred that cannot be recovered; irrelevant to the current operating decision.

𝑇𝐶(𝑞) = 𝑉𝐶(𝑞) + 𝐹𝐶

Marginal and average cost

MC is the slope of the total cost curve. AC is the slope of a ray ffrom the origin to a point on the total cost curve (secant method)

𝑀𝐶 = 𝛥𝑉𝐶/𝛥𝑞

Choosing output

Economic Profit: 𝜋(𝑞) = 𝑇𝑅(𝑞) − 𝑇𝐶(𝑞) = 𝑝𝑞 − 𝐶(𝑞)
Price taking firm: TR = pq and MR (marginal revenue) = p

IF MR > MC, expanding output increases profit at the margin. if MR < MC, reducing output increases profit

If the firm chooses to produce (positive interior optimum), choose output q where MR = MCq

Economic profit

Economic Profit: 𝜋(𝑞∗) = [𝑝 − 𝐴𝑇𝐶(𝑞∗)]𝑞∗
Profit or loss isrepresented by a rectangle with:

• base: the horizontal distance q* - 0

• height: the veritcal distance P - ATC(q*)

price above ATC(q*) indicates a profit; price below ATC(q*)

Producer surplus

Producer Surplus: PS(q*) = TR(q) -VC(q) = pq- VC(q)

Producer surplus is represented by a rectangle with:

• BAse: the horizontal distance q*-0

• Height: the vertical distance P-AVC(q*)

Price above AVC(q*) indicates a positive producer surplus

Prive below ACV(q*) indicates a negative producer surplus

Operating vs shutting down/exit

Operate if 𝜋(𝑞∗ > 0) ≥ 𝜋(0)

Shutdown: temporarily stop producing in the short run while continuing to pay unavoidable fixed costs. the firm is still in the market, just not producing

Exit: leave the market in the long run, avoiding future costs of operating. The firm has sold off all its assets.

Short run: shutdown decision

Produce if p > min SAVC: revenue exceed variable cost, so producer surplus is positive and helps cover fixed cost

Shut down if p < min SAVC: producing would generate negative producer surplus and a lrager loss than shutting down.

if p - min SAVC: producer surplus is zero; the firm is indifferent between producing and shutting down

Long run: exit decision

remain if p>min LRATC: revenue exceeds total economic cost, yielding positive economic profit

exit if p<min LRATC: revenue connat cover total economic cost

if p = min LRATC: economic profit is zero, including a normal return to the firm;s resources; the firm is indifferent between remaining and exiting

Short-run competitive firm supply