Question

Suppose a firm called, WeWorkTogether (Goal: profit maximization), has the following production function: Q = 2K ^0.4 L ^0.8.  Q: units of output, K: units of capital, L: units of labor.  If capital rents for $100 per unit per day, labor can be hired for $50 per unit per day, and the firm is minimizing costs,

a. Find the long-run total cost of producing Q= 50 units

b. Find the short-run total cost of producing Q= 50 units, when K is fixed at 10 units.

c. Explain how the short-run and long-run costs compare and why, using isoquants and isocost lines.

d. Find the algebraic expressions for the total cost (TC) (short-run and long-run) as a function of output and input prices.

e. If WeWorkTogether is operating in a perfectly competitive market, what is the minimum price below which the firm will shut down its production?  Below what price will the firm exit the market? What would be the profit maximizing output level if the market price of its output is $50/unit? What will be the profit or loss?

f. If you are the CEO of WeWokTogether, what would you be doing to avoid shut-down in the short run and to stay in the business in the long run?

Answer 1

Solution:-

Given that

  

LR Total Cost = VC + FC

= wL + r K

We have from demand function,

LR Total Cost = VC + FC

= wL + r K

  

LR Total Cost = VC + FC

= wL + r K

We have from demand function,

LR Total Cost = VC + FC

= wL + r K

LR Total Cost =

= 2254.50

SR Total Cost = 50 L + 100 K

= 1883.88

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