Production in LR

Features of LR production (ie differences to SR)

• K not fixed

• so PR function not just y-output , x-labour

• graph now 2D

LR production fnction (isoquant defn , how to solve)

• Isoquants→ all combos of K & L that give same lvl Q (output)

• How to solve : for a given Q₀ solve for K as fnction of L ( K = a/L)

Marginal rate of technical substitution (mrts eqn, in words , what is mrts measuring, what is it = to)

• MRTS = I delta K/ delta L I

• ie → abs val of slope of isoquant

• What is means → “how much L can we replace K w to make same level Q”

• delta K/ delta L (MRTS) = MPlabour/MPk

Returns to scale (why its a LR exclusive phenomenon, defn, inc decr constant rts + production fnc)

• LR thing cuz all inputs needa be able to change

• Returns to scale = how all of production responds to proprtional increase in all inputs

• Increasing rts → prop incr in all inputs = >proportional inc in output Q(cK,cL) > cQ(K,L)

• Decreasing rts →prop incr in all inputs = <proportional inc in output Q(cK,cL) < cQ(K,L)

• Constant rts →prop incr in all inputs = proportional inc in output Q(cK,cL) = cQ(K,L)

Diminishing vs decreasing rts (contrast , how will firms act, dr graphically isoquants

diminishing → sr , how output changes bcz of an increase in a specific factor

decreasing returns → lr , how incr in every factor affects total production

firms w dec,incr,constant rts still show diminishing returns

DR illustarted by how isoquants curved

The 3 production fnctions + diff times theyre used

1. Cobb-Douglas function (most common) → Q = mK^alpha L^beta m>0

In terms of RTS :

alpa + beta > 1 → increasing RTS

alpa + beta = 1 → constant RTS

alpa + beta < 1 → decreasing RTS

MRTS = (beta* K)/(alpaha *L)

Drawing Isoquant : set Q0 , rearrange for K & L

additional note on slide 21

2. Leontiff production function →K & L Perfect complements in pr (they needa incr in same proportion)→ Q= min { aK,bL}

inputs fixed in ratio to each other (cant make a complete unit w/o mainting ratio) so output take smallest value

line of efficient combos → input combos giving efficient output for this fnct type , MRTS dne here

grahs of Q @ right angles to each other

3. Straight line pr formula → Perfect subs in prod→ Q = aK + bL + c

constant MRTS

linear rlstinp btwn K & L