This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 7: Appendix CHAPTER 7 APPENDIX PRODUCTION AND COST THEORY A MATHEMATICAL TREATMENT EXERCISES 1. Of the following production functions, which exhibit increasing, constant, or decreasing returns to scale? a. F(K, L) = K 2 L b. F(K, L) = 10K + 5L c. F(K, L) = (KL) 0.5 Returns to scale refer to the relationship between output and proportional increases in all inputs. This is represented in the following manner (let >0) : F( K , L ) > F( K, L ) implies increasing returns to scale; F( K , L ) = F( K, L ) implies constant returns to scale; and F( K , L ) < F( K, L ) implies decreasing returns to scale. a. Applying this to F( K, L ) = K 2 L , F( K , L ) = ( K ) 2 ( L ) = 3 K 2 L = 3 F( K, L ). This is greater than F( K, L ); therefore, this production function exhibits increasing returns to scale. b. Applying the same technique to F( K, L ) = 10 K + 5 L , F( K , L ) = 10 K + 5 L = F( K, L ). This production function exhibits constant returns to scale. c. Applying the same technique to F( K, L) = ( KL ) 0.5 , F( K , L ) = ( K L ) 0.5 = ( 2 ) 0.5 ( KL ) 0.5 = ( KL ) 0.5 = F( K, L ). This production function exhibits constant returns to scale. 2. The production function for a product is given by q = 100KL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of output? The costminimizing combination of capital and labor is the one where MRTS MP MP w r L K = = . The marginal product of labor is dq dL = 100 K . The marginal product of capital is dq dK = 100 L . Therefore, the marginal rate of technical substitution is 100 100 K L K L = ....
View Full
Document
 Spring '11
 Prof.Eco

Click to edit the document details