A. Long Run vs. Short Run (40 pts) X=(1/2)L1/4K3/4, wL=$2, wK=$96 (dX/dL=(1/8)L-3/4K3/4, dX/dK= (3/8)L1/4K-1/4 1.(2...

A. Long Run vs. Short Run (40 pts) X=(1/2)L^1/4K^3/4, wL=$2, wK=$96 (dX/dL=(1/8)L^-3/4K^3/4,

dX/dK= (3/8)L^1/4K^-1/4

1.(2 pts)________________________________ For the point L=16 and K=81, what isoquant are we on?

2.(3 pts)___________________________________ From this point (L=16, K=81), to produce the same amount of X at a cheaper cost, should we use more L and less K OR less L and more K? Explain.

3. (3 pts)_________________________________Find the equation for the output expansion path.

4. (3 pts)_________________________________ Find the long run total cost function (total cost as a function of X alone)

5.(3 pts)_________________________________ Suppose K is stuck at K=16 in the short run. Find the short run total cost function. (total cost as a function of X alone) (Hint: Problem is easier if you keep answers in fractions)

6. (12 pts) Complete the following table for Point A, Point B, and Point C. (Fraction answers are possible)

Point A: The cheapest way to produce X=64

Point B: The cheapest way to produce X=64 when K is stuck in the short run at K=16

Point C. When we're producing X that gives us the lowest average cost when K is stuck in the short run at K=16

	L	K	X	TC	AC	MC
Point A
Point B
Point C

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

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A. Long Run vs. Short Run (40 pts) X=(1/2)L1/4K3/4, wL=$2, wK=$96 (dX/dL=(1/8)L-3/4K3/4, dX/dK= (3/8)L1/4K-1/4 1.(2...

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