Question

3. Suppose the production of Crocs is characterized by the production function Q = LK, where represents the number of pairs of Crocs produced. Suppose that the price of labor is $10 per unit and the price of capital is $1 per unit. a. Graph the isoquant for Q=121,000. b. On the graph you drew for part a, draw several isocost lines including one that is tangent to the isoquant you drew. What is the slope of the isocost lines? c. Find the cost-minimizing combination of labor and capital for a manufacturer that wants to produce 121,000 pairs of Crocs. Mark this point on the graph you drew for part a. d. Suppose, instead, that the technology for producing Crocs is described by Q=(L" +K12). Now what is the cost-minimizing combination of labor and capital for a manufacturer that wants to produce 121,000 pairs of Crocs?

Answer 1

Q3) a) isoquant

Q = LK= 121,000

w = 10, r = 1

Graph

K = 121,000/L

-8000 -6000- -4000– 2000 500 1000

B) Slope of isocost line = w/r = 10

-6000 -4000 Isocost lines -2000 100 200 300

C) at cost minimization

MRTS = w/r

MRTS = MPL/MPK = K/L

So at eqm, K/L = 10/1

K = 10L

So from Production function

121000 = 10L²

L* = 110

K* = 10L* = 1100

Graph

-4000 -2000 (110, 1100) 100 | | 200 300

.

D) new MRTS = MPL/MPK = √(K/L)

MPL = 2*(√L + √K)*(1/2)*L^{​​​​​​-1/2}

MPK = 2*(√L + √K)*(1/2)*K^{​​​​​-1/2}

.

At new eqm, MRTS = w/r

√(K/L) = 10

K/L = 100

K = 100L

From Production function

121,000 = (√L + √(100)L )²

√(121,000) = √L + 10√L

110√10 = 11√L

L* = 1000

K* = 100L* = 100,000