Submitted by: Submitted by bharatg
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Category: Business and Industry
Date Submitted: 10/29/2011 01:29 PM
7.2
A. True. When έQ < 1, the percentage change in output is less than a given percentage
change in all inputs. Thus, decreasing returns to scale and increasing average costs are
indicated.
B. True. Returns to the capital input factor are decreasing when the marginal product of
capital falls as capital usage grows
C. False. L-shaped production isoquants reflect a perfect complementary relation among
Inputs
D. False. Marginal revenue product is the revenue generated by expanding input usage and
represents the maximum that could be paid to expand usage. Since MRP is calculated
before input costs (wages in the case of labor, for example), it does not measure the
increase in profit earned through expansion.
E. False. The marginal rate of technical substitution is measured by the relative marginal
productivity of input factors. This relation is unaffected by a commensurate increase in
the marginal productivity of all inputs.
7.4
A. Q = 0.5X + 2Y + 40Z
Increase inputs by m,
Q’ = 0.5(X*m) + 2(Y*m) + 40(Z*m) = m*(0.5X + 2Y + 40Z)
Q’ = m* Q
Since Q’ = m*Q we note that by increasing all of our inputs by the multiplier m we've increased production by exactly m. So we have constant returns to scale.
B. Q = 3L + 10K + 500
Increase inputs by m,
Q’ = 3(L*m) + 10(K*m) + 500 = m*(3L + 10K) + 500
Q’ = m*Q + 500
Since, our new production has increased by more than m, so we have increasing returns to scale.
C. Q = 4A + 6B + 8AB
Increase inputs by m,
Q’ = 4(A*m) + 6(B*m) + 8(A*m)(B*m) = m * (4A + 6B + 8ABm)
D. Q = 7L2 + 5LK + 2K2
Increase inputs by m,
Q’ = 7(L*m)2 + 5(L*m)(K*m) + 2(K*m)2 = m2 * (7L2 + 5LK + 2K2)
If m <1, decreasing returns to scale
If m =1, constant returns to scale
If m >1, increasing returns to scale.
E. Q = 10L0.5 K0.3
Increase inputs by m,
Q’ = 10(L*m)0.5(K*m)0.3= 10L0.5 K0.3m0.8
Q’ = Q * m0.8
Since m > 1, then m0.8 < m. Our new production has increased by less than m, so we...