Short-run labor demand Ben and Jerry run an ice cream business in the town of Pa

Question

Short-run labor demand

Ben and Jerry run an ice cream business in the town of Palouse, WA. To produce the ice cream, they hire labor L at a wage of W dollars per worker. L is the only input in production. L workers produce Y pints of ice cream according to the production function,

They then sell the ice cream at the price of P dollars per pint of ice cream.

1.Plot the production function in a graph (with L on the X-axis and Y on the Y-axis) for

values of labor L = 0, ..., 10.

2. Write the firm’s profit function in terms of labor, ?(L). Then plot the firm’s profits for values of labor L=0,...,10 for price P =2 and wage W =4. From your graph, at what value of L do profits appear to be maximized?

Plot the MPL function for values of labor L = 0, ..., 10. How does the MPL change with the level of L employed? In this example, are there diminishing returns to labor?

4. State the condition on labor demand for which profits are maximized.

5. For the wage W = 4 and price P = 2, what is the profit maximizing level of labor demand,

L*?

6. Given the same price and wage as in Part 5, how many pints of ice cream do Ben and

Jerry produce under profit maximization (Y*)? What are their profits?

7. Now suppose Ferdinand’s starts selling ice cream in Palouse, which drives down the price that Ben and Jerry can get for a pint of their ice cream to P = 1. What is the new profit maximizing level of labor demand (L*)? Now how many pints are produced (Y*)? Now what are profits?

8. Is Ben and Jerry’s supply curve upward sloping between P = 1 and P = 2 (remember that a supply curve is the relationship between price P and optimal output Y*)?

Explanation / Answer

2. Profit(L) = 2(10L - (1/2)L2 ) - 4

For maximising profits differentiate above equation w.r.t L and equate it to 0

20 - 2L = 0

L = 10

3. MPL decreases with increase in L.

4. MPL = 0 and diminshing MPL

5. Same as part 2.

6. Y = 10(10) -(1/2) (10)(10) = 50

Profit = 2(50) - 4 = 96

7. profits = 1(10L -(1/2)L2) - 4

to maximise profits :

10 -L -4 =0

L = 6

Y = 42

Profits = 42(1) - 4 = 38

8. Yes, as the price have decreased output has also decreased.So we can say that supply cuve is positive sloping.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.