C3: Production and Supply

Question 1

What is the input cost & revenue of a firm in our model?

Answer 1

c = wL + rK
R(q) = pq

Question 2

What is the isocost line?

Answer 2

The line of input bundles incurring the same cost

Question 3

What is the isoquant?

Answer 3

Curve of all input bundles which yield the same production quantity q = F(L,K)

Question 4

What is the marginal rate of technical substitution?

Answer 4

Rate at which input 1 can be substituted for for input 2 at a point in the isoquant:

MRTS = dF/dL / dF/dK

also: the slope of the isoquant

Question 5

What are the returns to scale of a production function?

Answer 5

Scale inputs by constand x:
F(xK, xL) = y^a q

then if:
a < 1: decreasing returns
a = 1: constant returns
a > 1: increasing returns

Question 6

How can we describe the minimum production cost for a given quantity q as an optimization problem?

Answer 6

min_L,K wL + rK s.t. F(L,K) = q

interior solutions of the optimization problem have to satisfy:

MRTS = w/r

Question 7

List the important quantity w.r.t. cost

Answer 7

Total cost:
C(q) = c_f + c(q) // total cost = fixed + variable cost

Average cost:
a(q) = c(q) / q // average variable cost
A(q) = c_f / q + a(q) / q // average total cost

Short-Run vs. Long-Run total cost:
Long-Run total cost considers cost to be 0 if q = 0 (c_f must not be paid!; c_f is sunk cost for Short-Run total cost)

Marginal cost:
MC(q) = dC(q)/dq

Marginal revenue:
MR(q) = dR(q)/dq

Question 8

How can we formulate profit maximization as a constrained optimization problem?

Answer 8

max_q profit(q) = R(q) - C(q)

for an interior solution:
MC(q) = MR(q)

also: if price is fixed prior:
MR(q) = p

Question 9

What is the law of supply?

Answer 9

Ceteris paribus, the market supply of a good increases as its price increases: dQ/dp > 0