4. The following represents the long-run average total cost curves for 86 saving

Question

4. The following represents the long-run average total cost curves for 86 savings and loan associations in six northwestern states. Fora. use ?= .05. C 2.38-.00615 Q + .0000054Q' + 19.2 x, (standard errors) (0026) (.000002) (7.14) C = average operating expense ratio, expressed a % and defined as total operating expense ($million) divided by total assets ($million) times 100%. Q output measure by total assets (Smillion) Xi = ratio of the number of branches to total assets ($million) a. Which variables are statistically significant? b. Determine the level of assets that minimizes the average operating expense ratio. Where are the regions of economies and diseconomies of scale? c. For the Q found in b., fi nd the average operating expense ratio for a savings and loan wit i. one branch ii. 10 branches

Explanation / Answer

a)

df = n-k-1 = 86 -3-1 = 82

t-critical = 1.989

since every t-statisitic has magnitude more than 1.989

all variables are significant

b)

dC/dQ = 0

-0.00615 + 2 * 0.0000054 *Q = 0

Q = 569.444

c)

C = 2.38 -0.00615 Q+ 0.0000054 *Q^2 + 19.2 X1

Q = 569.444

if i) X1 = 1

then

C = 2.38 -0.00615 Q+ 0.0000054 *Q^2 + 19.2 X1

= 2.38 -0.00615 *569.444 + 0.0000054 *569.444 ^2 + 19.2 *1

= 19.8289583333

ii) X1 = 10

C = 2.38 -0.00615 Q+ 0.0000054 *Q^2 + 19.2 X1

= 2.38 -0.00615 *569.444 + 0.0000054 *569.444 ^2 + 19.2 *10

=192.628958333

Q -0.00615 0.0026 -2.36538 Q^2 0.0000054 0.000002 2.7 X1 19.2 7.14 2.689076

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