This problem parallels the previousone, 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 afirm'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 previousproblem, 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 ofQ, using the exponent rules from above. This relationship gives thecost-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 afraction). Since K= L, the same function gives K as a function ofQ: 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 byC(Q) = gQh, where g=

nothing

and h=

nothing

(enter the exponent as afraction).

d) The average cost functionAC(Q) is equal to cost divided byoutput, orC(Q)/Q. Using your solution forC(Q), it follows thatAC(Q) = aQm, where a=

nothing

and m=

nothing

(enter asfraction, and include a minus sign if one isneeded). Graphing AC as a function ofQ, the result is

A.

an upward sloping curve

B.

a downward sloping curve

C.

a horizontal line

e) Marginal costMC(Q) is given by the derivative ofC(Q). If you remember how to compute the derivative of a function like gQh , then do so. The resulting MC function has the formMC(Q) = zQr, where z=

nothing

and r=

nothing

. The MC curve lies

A.

above the AC curve

B.

below the AC curve