Question

Please show all work.

Thanks.

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)-101-9L 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,., 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 MP, function (AY/AL) for the production function given above is: MPAL-10-L. Plot the MPh function for values of labor L 0, , 10. How does the MP, 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, 6. Given the same price and wage as in Part 5, how many pints of ice cream do Bhen and 7. Now suppose Ferdinand's starts selling ice cream in Palouse, which drives down the price L-? Geri produce under profit maximization (*)? What are their profits? 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)?

Answer 1

Given, been and give runs an ice cream business in town w_a to produce ice cream they hire, labor - L wages - w and y = F(L) = 10L - 1/2 L^2 y = ice-cream produced and sell ice-cream at p dollars per point of ice-cream. Plot the production function in graph with L on x axis and y on y axis for values L = 0,1,2,...10) for L = 0 y = f(L) = 0 L = 1, y = f(L) = 10 - 1/2 = 19/2 = 9.5 L = 2, Y = F(L) = 20 - 1/2 = 18 L = 3, \r\n y = F(L) = 10(3) + 1/2(3)^2 = 30 - 9/2 = 30 - 4.5 = 25.5 L = 4, Y = F(L) = 10(4) - 1/2(4)(4) = 40 -8 = 32 L = 5., Y = (F(L)) = 10(5) - 1/2(25) = 50- 12.5 = 37.5 L = 6, Y = F(L) = 10(6) - 1/2 (6)(6) = 60 - 18 = 42 L = 7, Y = F(L)) = 10(7) - 1/2(7)(7) = 70 - 24.5 = 45.5 L = 8, Y = F(L) = 10(8) - 1/2(8)(8) = 80 - 32 = 48 L = 9, Y = F(L) = 10(9) - 1/2(9)(9)