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Bhen and Geri 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, Y = F(L) = 10L − ( 1 2 )L 2 . 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, Π(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? 3. The MPL function (∆Y/∆L) for the production function given above is: MPL(L) = 10 − L. 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 Bhen and Geri 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 Bhen and Geri 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 Bhen and Geri’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 ∗ )?
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