In doing this problem, it helps to remember a few rule about exponents. The first rule is that, for any positive number B, (B B (in words, B raised to the power n raised to the power s equals B raised to the power n times s). Two other rules are B B (B raised to the power one just equals B), and B1 (B raised to the power zero equals 1). You'll need to use each of these rules below K1L1/2= ( KL) 12 a) Suppose that a firm's production function is given by Q This production function exhibits O A. constant returns to scale B. increasing returns to scale O C. decreasing returns to scale b) Suppose that r w 2, so that production cost in terms of K and L can be written 2K+ 2L. Just as in that previous problem, the isoquant slope MP, MP is equal isocost line yields K L. Substitute K L in the production function Q (KL)1. Then use the resulting equation to solve for L as a function of Q, using the exponent rules from above. This relations hip gives the cost-minimizing L as a function of Q. This function has the form L bQwhere the multiplicative factor b |and the exponent d (use the above exponent rules). Since K L, the same function gives K as a function of Q: K bQ -KL, so that equating the isoquant slope to the -1 slope of the c) Now substitute your solutions into the cost expression 2K+ 2L to get cost C as a function of Q. This function is given by C(Q) gQ", where g and h = d) The average cost function AC(0) is equal to cost divided by output, or C(QyQ. Using your solution for C(Q), it follows that AC(Q) am where a and m Graphing AC as a function of Q, the result is O A. a horizontal line O B. an upward sloping ourve O C. a downward sloping curve Marginal cost MC(Q) is given by the derivative of C(Q), but it can also be derived as the increase in cost when Q goes up by 1 unit. Using either approach, MC(Q) z and r=The MC curve is where z O A. a horizontal line higher than the AC curve O B. an upward sloping ourve O C. a horizontal line that coincides with the horizontal AC curve O D. a downward sloping ourve
In doing this problem, it helps to remember a few rule about exponents. The first rule is that, for any positive number B, (B B (in words, B raised to the power n raised to the power s equals B raised to the power n times s). Two other rules are B B (B raised to the power one just equals B), and B1 (B raised to the power zero equals 1). You'll need to use each of these rules below K1L1/2= ( KL) 12 a) Suppose that a firm's production function is given by Q This production function exhibits O A. constant returns to scale B. increasing returns to scale O C. decreasing returns to scale b) Suppose that r w 2, so that production cost in terms of K and L can be written 2K+ 2L. Just as in that previous problem, the isoquant slope MP, MP is equal isocost line yields K L. Substitute K L in the production function Q (KL)1. Then use the resulting equation to solve for L as a function of Q, using the exponent rules from above. This relations hip gives the cost-minimizing L as a function of Q. This function has the form L bQwhere the multiplicative factor b |and the exponent d (use the above exponent rules). Since K L, the same function gives K as a function of Q: K bQ -KL, so that equating the isoquant slope to the -1 slope of the c) Now substitute your solutions into the cost expression 2K+ 2L to get cost C as a function of Q. This function is given by C(Q) gQ", where g and h = d) The average cost function AC(0) is equal to cost divided by output, or C(QyQ. Using your solution for C(Q), it follows that AC(Q) am where a and m Graphing AC as a function of Q, the result is O A. a horizontal line O B. an upward sloping ourve O C. a downward sloping curve Marginal cost MC(Q) is given by the derivative of C(Q), but it can also be derived as the increase in cost when Q goes up by 1 unit. Using either approach, MC(Q) z and r=The MC curve is where z O A. a horizontal line higher than the AC curve O B. an upward sloping ourve O C. a horizontal line that coincides with the horizontal AC curve O D. a downward sloping ourve
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Transcribed Image Text:In doing this problem, it helps to remember a few rule about exponents. The first rule is that, for any positive number B, (B B (in words, B raised to the power n raised to the power s equals B raised to the power n times s).
Two other rules are B B (B raised to the power one just equals B), and B1 (B raised to the power zero equals 1). You'll need to use each of these rules below
K1L1/2= ( KL) 12
a) Suppose that a firm's production function is given by Q
This production function exhibits
O A. constant returns to scale
B. increasing returns to scale
O C. decreasing returns to scale
b) Suppose that r w 2, so that production cost in terms of K and L can be written 2K+ 2L. Just as in that previous problem, the isoquant slope MP, MP is equal
isocost line yields K L. Substitute K L in the production function Q (KL)1. Then use the resulting equation to solve for L as a function of Q, using the exponent rules from above. This relations hip gives the cost-minimizing L
as a function of Q. This function has the form L bQwhere the multiplicative factor b |and the exponent d (use the above exponent rules). Since K L, the same function gives K as a function of Q: K bQ
-KL, so that equating the isoquant slope to the -1 slope of the
c) Now substitute your solutions into the cost expression 2K+ 2L to get cost C as a function of Q. This function is given by C(Q) gQ", where g
and h =
d) The average cost function AC(0) is equal to cost divided by output, or C(QyQ. Using your solution for C(Q), it follows that AC(Q) am where a and m
Graphing AC as a function of Q, the result is
O A.
a horizontal line
O B. an upward sloping ourve
O C. a downward sloping curve
Marginal cost MC(Q) is given by the derivative of C(Q), but it can also be derived as the increase in cost when Q goes up by 1 unit. Using either approach, MC(Q) z
and r=The MC curve is
where z
O A. a horizontal line higher than the AC curve
O B. an upward sloping ourve
O C. a horizontal line that coincides with the horizontal AC curve
O D. a downward sloping ourve
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