= 3.2 Now consider the production function of an additional product, electrical generators, de- fined by the following function: Qeg K0.6L04 Show, using the Jacobian derivative matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units, would approximately change production of both goods. Start from an initial combination of K=100 and L = 50. 3.3 Suppose that demand for capital and labour are in turn determined by the interest rate r and wages paid to workers w, as follows: K = 8 and L = 1252. Use the Jacobian derivative matrix of Qe and Qeg to calculate how production changes in response to an მი Or increase in interest rates: DQeg Or 103 when 2 and w = 1000. =
= 3.2 Now consider the production function of an additional product, electrical generators, de- fined by the following function: Qeg K0.6L04 Show, using the Jacobian derivative matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units, would approximately change production of both goods. Start from an initial combination of K=100 and L = 50. 3.3 Suppose that demand for capital and labour are in turn determined by the interest rate r and wages paid to workers w, as follows: K = 8 and L = 1252. Use the Jacobian derivative matrix of Qe and Qeg to calculate how production changes in response to an მი Or increase in interest rates: DQeg Or 103 when 2 and w = 1000. =
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Any help with 3.2 and 3.3
![3 Consider the production function of candles, with capital (K) and labour (L) as inputs:
Qc = K0.1 L0.9.
3.1 Show that both additional labour and additional capital increase production at a decreasing
rate by computing and referring to some of the second derivatives of Qe.
3.2 Now consider the production function of an additional product, electrical generators, de-
fined by the following function: Qeg
= K0.6 L0.4. Show, using the Jacobian derivative
matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units,
would approximately change production of both goods. Start from an initial combination
of K = 100 and L = 50.
3.3 Suppose that demand for capital and labour are in turn determined by the interest rate
125. Use the Jacobian
r and wages paid to workers w, as follows: K =
derivative matrix of Qe and Qeg to calculate how production changes in response to an
and L =
10r3
ar
increase in interest rates:
when r = 2 and w = 1000.
Or](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e234871-73b8-4b63-8f58-d73ac884ead5%2Ffdd12f64-32c8-4331-95db-1dec10c0932c%2F6f18f2w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3 Consider the production function of candles, with capital (K) and labour (L) as inputs:
Qc = K0.1 L0.9.
3.1 Show that both additional labour and additional capital increase production at a decreasing
rate by computing and referring to some of the second derivatives of Qe.
3.2 Now consider the production function of an additional product, electrical generators, de-
fined by the following function: Qeg
= K0.6 L0.4. Show, using the Jacobian derivative
matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units,
would approximately change production of both goods. Start from an initial combination
of K = 100 and L = 50.
3.3 Suppose that demand for capital and labour are in turn determined by the interest rate
125. Use the Jacobian
r and wages paid to workers w, as follows: K =
derivative matrix of Qe and Qeg to calculate how production changes in response to an
and L =
10r3
ar
increase in interest rates:
when r = 2 and w = 1000.
Or
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