Question

1. Suppose the cost of labor rises by 25% and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm’s expansion path. (7 pts)

2. Suppose that a firm’s production function is q = 2L^1/2K^1/2. The cost of a unit of labor is $18.50 and the cost of a unit of capital is $20. The firm is currently producing 1,000 units of output and has determined that the cost minimizing quantities of labor and capital are 100 and 20, respectively. Write the function form of isoquant (K as a function of L, given q = 1,000). Also write the function form of isocost. (8 pts)

3. Give an example of an implicit opportunity cost, based on observation in your daily life, as a student, a worker, or an entrepreneur. Implicit cost is cost that does not require an outlay of money. (6 pts)

Answer 1

(1) Due to increase in cost of labour the slope of isocost curve will increase and they will pivot inside from orange isocost lines to blue isocost lines. The new tangency conditions for cost minimization is shown at point A' and B' joining which we get our new expansion path shown by black straight line passing through origin. We see that compared to original expansion path (Red straight line passing through origin) relatively more capital is used than labour along the new expansion path. This happens due to relative increase in the price of labour.   

(2) Isoquant given q=1000:

  

We have, cost of a unit of labour (w) = $18.50, cost of a unit of capital (r) = $20

cost minimizing quantity of labour (L) =100 and cost minimizing quantity of capital (K) =20  

  Total cost of producing (q=1000) = wL+rK = $18.50 (100) + $20 (20) = $2250.

Isocost when cost = $2250:

  

(3)

Profession	Implicit Cost
Student	Wage lost not working at the market wage with the present qualifications
Worker	Profits he/she can earn doing his/her own business
Entrepreneur	Wage that he/she could earn as an employ working in other firm