Lindsey\'s Pretzel plant has the following short-run function: C(q,K) = (wq^3) /

Question

Lindsey's Pretzel plant has the following short-run function: C(q,K) = (wq^3) / (1,000K^1.5) + 50K

Where q is Lindsey's output level, w is the cost of a labor hour, and K is the number pretzel machines Lindsey leases. Lindsey's short-run marginal cost curve is MC(q,K) = (3wq^2) / 1000K^1.5

At the moment, Lindsey leases 10 pretzel machines, the cost of a labor hour is $6.85, and she can sell at the output she produces at $35 per unit.

a. Determine Lindsey's profit/loss.

b. If the cost per labor hour rises to $7.50, what happens to Lindsey's optimal level of output and profit?

Explanation / Answer

a. At optimal condition MR=MC

So, 35=3x6.85q2/1000k1.5

or, 35000k1.5=20.55q2

or, q=1703.16(k1.5)0.5

b. If cost of labour hour rises to $7.50 then,

q=35000/(7.50x3) x (k1.5)0.5

or, q=1555.55(k1.5)0.5

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.