# 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 = Bs-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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