Managerial Economic Analysis

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...