1) Suppose that a firm's output is determined by the amount of labor (L) it hires...

 

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1) Suppose that a firm's output is determined by the amount of labor (L) it hires according to function: q= 2√L. Suppose that the firm can hire all the labor it wants at $10 per unit and sells its output at $50 per unit. Profits are therefore a function of L given (L) =100V/L-10L. a) Compute L* (5 pts.) b) What is the profit at L*? (5 pts.) 2) Suppose that Y is a function of X₁ and X₂ given by Y = -(x1-1)²-(x2-2)²+10 or Y = -x₁²+2x1-X₂²+4x2+5 Suppose Y = represent an individual's health (on a scale of 0-10) and X₁ and X₂ are the daily dosage of two health-enhancing drugs. a) Find the value of X₁ and X₂ that will make Y as large as possible. (15 pts.) 3) Suppose that the relationship between profits (1) and the quantity produced (q) is given by: n(q) = 1000q-5q² a) What is the value of q* that maximizes profits? (5 pts.) b) Given q*, what is the highest possible value of the profit? (5 pts.) c) What if the firm decided to: c.1) produce q=50, what would the profit be? (5 pts.) c.2) produce q=200, what would the profit be? (5 pts.) d) At q*, is it a global maximum or minimum? Qualify your answer. (15 pts) 1) Suppose that a firm's output is determined by the amount of labor (L) it hires according to function: q= 2√L. Suppose that the firm can hire all the labor it wants at $10 per unit and sells its output at $50 per unit. Profits are therefore a function of L given (L) =100V/L-10L. a) Compute L* (5 pts.) b) What is the profit at L*? (5 pts.) 2) Suppose that Y is a function of X₁ and X₂ given by Y = -(x1-1)²-(x2-2)²+10 or Y = -x₁²+2x1-X₂²+4x2+5 Suppose Y = represent an individual's health (on a scale of 0-10) and X₁ and X₂ are the daily dosage of two health-enhancing drugs. a) Find the value of X₁ and X₂ that will make Y as large as possible. (15 pts.) 3) Suppose that the relationship between profits (1) and the quantity produced (q) is given by: n(q) = 1000q-5q² a) What is the value of q* that maximizes profits? (5 pts.) b) Given q*, what is the highest possible value of the profit? (5 pts.) c) What if the firm decided to: c.1) produce q=50, what would the profit be? (5 pts.) c.2) produce q=200, what would the profit be? (5 pts.) d) At q*, is it a global maximum or minimum? Qualify your answer. (15 pts)

Answer rating: 100% (QA)

1 a To find the value of L that maximizes profits we need to find the value of L that maximizes piL We can do this by taking the derivative of piL wit... View the full answer