In doing thisproblem, it helps to remember a few rule about exponents. The first rule isthat, for any positive numberB, (Bn)s= Bns (in words, B raised to the power n raised to the power s equals B raised to the power n timess). Two other rules are B1= B(B raised to the power one just equalsB), and B0= 1(B raised to the power zero equals1). You'll need to use each of these rules below.

a) Suppose that afirm's production function is given by Q= K1/2L1/2= (KL)1/2. This production function exhibits

A.

increasing returns to scale

B.

constant returns to scale

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 previousproblem, 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)1/2 . 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

(use the above exponentrules). 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

.

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

. Graphing AC as a function ofQ, the result is

A.

a downward sloping curve

B.

a horizontal line

C.

an upward sloping curve

Marginal costMC(Q) is given by the derivative ofC(Q), but it can also be derived as the increase in cost when Q goes up by 1 unit. Using eitherapproach, MC(Q)= zQr, where z=

nothing

and r=

nothing

. The MC curve is

A.

a downward sloping curve

B.

an upward sloping curve

C.

a horizontal line higher than the AC curve

D.

a horizontal line that coincides with the horizontal AC curve