Homer\'s boat manufacturing plant production function is y(K,L) = (K^1/2 ) (L^1/
ID: 1210374 • Letter: H
Question
Homer's boat manufacturing plant production function is y(K,L) = (K^1/2 ) (L^1/5) where K is the number of hyraulic lifts and L is the number of labor hours he employs.
a. Does this production function exhibit increasing, decreasing or constant returns to scale?
b. At the moment, Homer uses 20,000 labor hours and 50 hydraulic lifts. Suppose that Homer can use any amount of either input without affecting the market costs of inputs. If Homer increase his use of labor hours and hyrdaulic lifs by 10%, how much would his production increase?
c. Increasing the use of both inputs by 10% will result in Homer's cost increasing by exactly 10%. If Homer increases his use by all inputs by 10%, what will increase more, his production or his costs?
d. Given that Homer can sell as many boats as he produces for $75,000, does his profits go up by 10% with a 10% increase in input use?
Explanation / Answer
a. Does this production function exhibit increasing, decreasing or constant returns to scale?
y(K,L) = (K^1/2 )(L^1/2)
Increasing each variable by
y(K,L) = (K^1/2 )(L^1/2)
Y(K,L) = 1/2(K^1/2)1/2(L^1/2)
Y(K,L) = (K^1/2 )(L^1/2)
So, Constant returns to scale
b. At the moment, Homer uses 20,000 labor hours and 50 hydraulic lifts. Suppose that Homer can use any amount of either input without affecting the market costs of inputs. If Homer increase his use of labor hours and hyrdaulic lifs by 10%, how much would his production increase?
Since the production function exibits constant returns to scale, So Production will also increase by 10%
c. Increasing the use of both inputs by 10% will result in Homer's cost increasing by exactly 10%. If Homer increases his use by all inputs by 10%, what will increase more, his production or his costs?
Both production and cost will increase in same proportion
d. Given that Homer can sell as many boats as he produces for $75,000, does his profits go up by 10% with a 10% increase in input use?
No. as with a 10% increase in input use, Cost of inputs will also go up by 10%.
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