The economic planning department at international chemicals inc has used regress
ID: 1121903 • Letter: T
Question
The economic planning department at international chemicals inc has used regression analysis to estimate the firm's production function as ln Q = 3 + .25 ln K + .75 ln L
a. Convert the production function back to its original(Multiplicative or Cobb- Douglas) form. (Hint: Find the antilogarithm of both sides of the equation)
b. If the capital stock is fixed at 16, the price of labor is $200 per unit, and the price of the firm's only product, sulfuric acid, is $10 per unit, determine the rate of labor input that will maximize the firm's profit.
Explanation / Answer
a) ln Q = 3 + 0.25 lnK + 0.75 L
Anti log on both sides
anti log (ln Q) = anti log ( ln e3 + ln K 0.25 + ln L0.75 ) [ ln ab = b ln (a) ]
Q = anti log ( ln ( e3 K 0.25 L0.75 ) ) [ ln a + ln b + ln c = ln (abc) ]
Q = e3 K 0.25 L0.75
value of e = 2.718
e3 = 20.09
Q = 20.09 K 0.25 L0.75
Q = productivity
K = capital = 16
L = labour = 200
Q = 20.09 x 16 0.25 x 2000.75
Q = 2136.89
Rate of labour input = Q/ L = 2136.89/200
Rate of labour input = 10.68 hours
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