Question

1. Suppose the production of digital cameras is characterized by the production function q F(K, L)- KL (MPL = K, MPK = L), where q represents the number of digital cameras produced. Suppose that the price of labor is $10 per unit and the price of capital is S1 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) Calculate the cost - minimizing combination of labor and capital for a manufacturer that wants to produce 121,000 digital cameras. Mark this point on the graph you drew for part a). 2. Walter and Jesse operate a car wash, where labor (L) and car wash conveyor belts (K) are the two inputs. In order to produce one car wash (q). Walter and Jesse must use at least 3 units of labor and at

Answer 1

A) as Q= K*L

K = Q/L= 121,000/L

Isoquant: K = 121,000/L

4000 soquant 3000 isocost lines 2000 equilibrium combination (110, 1100) 1000 200 400 600 Labor

b) isocost line , C = L*w + K*r

so C = 10L + K

slope of isocost line = w/r = 10

c) at cost minimising combination,

MRTS_​​​L,K = w/r

as MRTS= MPL/MPK= K/L

so at eqm, K/L = 10

so K = 10L

now from Production function,

121,000 = 10L²

thus L = 110

Hence K = 1,100

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