Production and costs

Question 1

Production function

Answer 1

Q = f(K, L)

Q : output
K : capital input (building, machinery)
L : Labour input (employee)

Question 2

short run : production function

Answer 2

K is fixed
L is flexible

Question 3

long run: production function

Answer 3

(K, L) are flexible

Question 4

Marginal product of labor and capital

Answer 4

∂Q(K, L) / ∂L = MPL

∂Q(K, L) / ∂K = MPK

Question 5

isoquant

Answer 5

curve represents all combinations of inputs that allow a firm to produce a particular quantity of output.

Question 6

marginal rate of technical substitution (MRTS)

Answer 6

is the negative value of the slope of the isoquant at a particular point

Question 7

An isocost line

Answer 7

shows all of the input combinations that yield the same cost.

Question 8

For a particular total cost level of C, the isocost line is:

Answer 8

C = RK + WL

R: the price per unit of capital (depreciation and interest rate)

W: the price per unit of labor (opportunity costs)

Question 9

Solving for K (on the vertical axis) yields the downward-sloping straight line

Answer 9

K = R /C − WR / L

Question 10

The cost-minimizing input combination satisfies two requirements:

Answer 10

– It lies on a given isoquant
– It lies on the lowest possible isocost line

Question 11

At the optimal input combination, the isocost line is..

Answer 11

tangent to the isoquant (“tangency condition”), i.e. the slopes are equal

Question 12

cost function

Answer 12

shows the minimum production cost for the output at the given input prices.

The cost function is therefore the sum of the conditional demands for the inputs weighted by the input prices.

Question 13

The cost function is given by

Answer 13

C(W, R, Q) = WL(W, R, Q) + RK(W, R, Q)

Question 14

How does output change if all inputs are increased? (Returns to scale)

Answer 14

Constant returns to scale –> Output rises proportionately

Increasing returns to scale –> Output rises more than proportionately

Decreasing returns to scale –> Output rises less than proportionately

Question 15

How does cost change if output is increased?

Answer 15

Constant economies of scale –> Cost rises proportionately

Economies of scale –> Cost rises less than proportionately

Diseconomies of scale –> Cost rises more than proportionately

Question 16

If factor prices are given, the cost function C(W, R, Q) is often simply denoted by …

Answer 16

C(Q)

Question 17

If the firm chooses both output Q and product carbon footprint κ,we denote the cost function by…

Answer 17

C(Q, κ)

Question 18

Constant marginal cost

Answer 18

• With constant marginal cost, we have ∂C(Q,κ) / ∂Q ≡ c(κ)
• If production with high (low) CO2 emissions is cheap (expensive), we have c′(κ) < 0.

Question 19

conditional demand for inputs

Answer 19

the amount of each input (like labor L and capital
k) that a firm requires to minimize its costs while producing a given level of output, q at given input prices.

Question 20

cost function

Answer 20

summing the product of the optimal quantity and the respective cost of each input

Question 21

Long- run demands for capital and labor, how is the capital?

Answer 21

In the long run K is fix