This problem parallels the previousone, but uses a different production function. Also, you'll need one more exponent rule in addition to those given...
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This problem parallels the previous​ one, but uses a different production

function. ​ Also, you'll need one more exponent rule in addition to those given in the previous problem. The rule is Bs​/B ​= B​s-1.
​a) Suppose that a​ firm's production function is given by Q​ = KL. If this production function exhibits
A.
increasing returns to scale
B.
constant returns to scale
C.
decreasing returns to scale
​b) As in the previous​ problem, suppose that r​ = w​ = 2, so that production cost in terms of K and L can be written 2K​ + 2L. The isoquant slope MPL​/MPK is equal to​ -K/L , so that equating the isoquant slope to the​ -1 slope of the isocost line yields K​ = L. Substitute K​ = L in the production function Q​ = KL . Then use the resulting equation to solve for L as a function of​ Q, using the exponent rules from above. This relationship gives the​ cost-minimizing L as a function of Q. This function has the form L​ = bQd​ , where the multiplicative factor b​ =
nothing


and the exponent d​ =
nothing


​(enter the exponent as a​ fraction). Since K​ = L, the same function gives K as a function of​ Q: K​ = bQd.
​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) = gQh​, where g​ =
nothing


and h​ =
nothing


​(enter the exponent as a​ fraction).
​d) The average cost function​ AC(Q) is equal to cost divided by​ output, or​ C(Q)/Q. Using your solution for​ C(Q), it follows that​ AC(Q) = aQm​, where a​ =
nothing


and m​ =
nothing


​(enter as​ fraction, and include a minus sign if one is​ needed). Graphing AC as a function of​ Q, the result is
A.
an upward sloping curve
B.
a downward sloping curve
C.
a horizontal line
​e) Marginal cost​ MC(Q) is given by the derivative of​ C(Q). If you remember how to compute the derivative of a function like gQh ​, then do so. The resulting MC function has the form​ MC(Q) = zQr​ , where z​ =
nothing


and r​ =
nothing


. The MC curve lies
A.
above the AC curve
B.
below the AC curve

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