Ch 20-21 Profit Max & Cost Min

Question 1

Marginal revenue (short run)

Answer 1

P(MPL)= marginal revenue

Question 2

Long-run profit max formula

Answer 2

π=pF(L,K)-wL-rK

For profit maximizing choices for LNK the value of the marginal product of labor and capital should be equal to the price of labor and capital

pMPL=w
pMPK=r

If we rearrange the equations:
P=w/(MPL), p=r/(MPK)

➡️MPL/MPK=w/r thus MRTS=w/r

Question 3

Wage elasticity of SR labor

Answer 3

ε=ρL/ρω *ω/L

Question 4

Shut-Down decision

Answer 4

In the short run a firm will operate as long as π=pF(L,K)-ωL-rK >rK or pF(L,K)-ωL>0

i.w if profit exceeds fixed costs or if profit minus the cost of labor (variable costs) is greater than zero

In the long run a firm will only operate if π=pF(L,K)-ωL-rK>0

always test for shut down in the LR cost min

Question 5

Average cost

Answer 5

Average cost is the per unit cost to produce Q units of output

AC= AC(Q,w,r) =TC/Q

And AC*Q= TC

Question 6

Average cost and returns to scale

Answer 6

CRS: AC(Q1,w,r)=AC(Q2,w,r)

IRS: AC(Q1,w,r)>AC(Q2,w,r)
AC is decreasing as we continue to produce

DRS: AC(Q1,w,r)

Question 7

Profit formula (profit max SR)

Answer 7

π=pF(L,K)-wL-rK

pMPL=w in the short run

Conditions that must be met:
P=MC
MC is increasing at this point