1. The following table shows data for a simple production function.
Capital(K) Labor(L) Total Product(TP) Average Product(AP) Marginal Product(MP)
Column 1 numbers = Capital ; Column 2 numbers = Labor; Column 3 numbers= Total Product
10 0 0
10 1 5
10 2 15
10 3 30
10 4 50
10 5 75
10 6 85
10 7 90
10 8 92
10 9 92
10 10 90
a. From the information in the table, calculate marginal and average products.
b. Graph the three functions on separate graphs (Total production, Marginal Products and Average Products).
c. For what range of output does this function have diminishing marginal returns?
d. At what output is average product maximized?
2. Suppose the demand curve for a monopolist is QD= 500 - P, and the marginal revenue function is MR = 500 - 2Q. The monopolist has a constant marginal and average total cost of $50 per unit.
a. Find the monopolist's profit-maximizing output and price.
b. Calculate the monopolist's profit.
c. What is the Lerner Index for this industry?
a) See the attached Excel file.
b) See the attached Excel file.
c) The range L > 5
d) When L = 5 and AP = 25
a) Profit is maximized when ...
This solution gives detailed calculations showing how to:
1. Calculate marginal and average product, graph the resulting functions, and use the data to determine the maximum average product.
2. Calculate a monopolist's profit-maximizing price, output and profit, and use the result to determine the Lerner Index for the industry.