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# tutorial_7ans - ECOS 2001 Tutorial 7 1 3 1 Suppose that the...

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ECOS2001 Tutorial 7 1 ECOS 2001 Tutorial 7 1. Suppose that the production function is Cobb-Douglas and ( ) 12 32 12 1 2 , fxx xx = . 1. Write an expression for the marginal product of 1 x at the point () , x x . 2. The marginal product of 1 x (increases, decreases, remains constant?) for small increase in 1 x , holding 2 x constant. 3. An increase in the amount of 2 x (increase, leaves unchanged, decreasing?) the marginal product of 1 x . 4. What is the technical rate of substitution (TRS) between 2 x and 1 x ? 5. What is the TRS between 2 x and 1 x at the point ( ) 3, 2 ? 6. Does this technology have diminishing TRS? 7. This technology demonstrates (increasing, constant, decreasing?) returns to scale. 1. 1 3/2 2 11 2 1 2 M Px x =− 2. decreases 3. 1 1/2 2 21 2 3 2 M x = ; increases for small increases in x2 4. TRS 21 = -x 2 /3x 1 5. TRS (x 1 =3,x 2 =2) = 2/(3.3) = 2/9 6. Yes 7. increasing 2. The Ontario Brassworks produces brazen effronteries. Brass is an alloy of copper ( 1 x ) and zinc ( 2 x ), used in fixed proportions. The production function is given by { } 1 2 ,m i n , 2 x x = . 1. Draw a few isoquants for this production function. 2. Is this technology convex? 3. Does this production function exhibit increasing, decreasing, or constant returns to scale? 4. If the firm wanted to produce 10 effronteries, how much copper would it need? How much zinc would it need?

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## This note was uploaded on 04/20/2010 for the course ECOS 2001 taught by Professor None during the One '09 term at University of Sydney.

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tutorial_7ans - ECOS 2001 Tutorial 7 1 3 1 Suppose that the...

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