The production function for orange juice is:

Q = 60L - L²

Orange juice sells for $2 per unit. The cost of each unit of labor (L) is $20 per hour.

a. What is the optimal amount of labor (L) to hire?

b. If the company raises their price to $4, what would the optimal amount of (L) to hire?

c. Assume the workers unionize and increase the wage to $24 per hour (the price is back to $2). What

would happen to the optimal amount of labor to hire? Explain.

d. Now the firm adds machines to its production process. The new production function is:

Q = 60L - L² + 90K - K²

Orange juice sells for $2 per unit. The cost of each unit of labor (L) is $20 per hour, and the cost of each

unit of capital (K) is $30 per hour.

What of the two inputs is initially more productive? Explain.

e. With a budget of $1,950, what is the optimal amount of labor (L) and capital (K) to employ?

f. Assume you have a budget of $500. Which production process would produce more output - the

function with labor only (part a) or the function with labor and capital (part d)? Prove this

mathematically. (Orange juice sells for $2 per unit. The cost of each unit of labor (L) is $20 per hour,

and the cost of each unit of capital (K) is $30 per hour.)