Problem 1: Consider a perfectly competitive industry composed of N identical firms in the short run. The firm produces output, q, using labor (L) and capital (K): q=√LK In the short run, each firm's capital is fixed at one unit. Each unit of labor and capital cost w and r respectively. The industry demand curve is given by: P=a-Q, a>0 1. Find the short run equilibrium price, firm output, and industry output. 2. How will the short run equilibrium price and outputs vary with a change in the wage rate, w? Explain your answer. 3. How will the short run equilibrium price and outputs vary with a change in the rental rate, r? Explain your answer.

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Problem 1: Consider a perfectly competitive industry composed of N identical
firms in the short run. The firm produces output, q, using labor (L) and capital
(K):
q= √LK
In the short run, each firm's capital is fixed at one unit. Each unit of labor
and capital cost w and r respectively. The industry demand curve is given by:
P=a-Q, a>0
1. Find the short run equilibrium price, firm output, and industry output.
2. How will the short run equilibrium price and outputs vary with a
change in the wage rate, w? Explain your answer.
3. How will the short run equilibrium price and outputs vary with a
change in the rental rate, r? Explain your answer.
Transcribed Image Text:Problem 1: Consider a perfectly competitive industry composed of N identical firms in the short run. The firm produces output, q, using labor (L) and capital (K): q= √LK In the short run, each firm's capital is fixed at one unit. Each unit of labor and capital cost w and r respectively. The industry demand curve is given by: P=a-Q, a>0 1. Find the short run equilibrium price, firm output, and industry output. 2. How will the short run equilibrium price and outputs vary with a change in the wage rate, w? Explain your answer. 3. How will the short run equilibrium price and outputs vary with a change in the rental rate, r? Explain your answer.
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