# Managerial Econ: Marginal Revenue Cost of Labor/Price Elasticity

7. Problem-solving question: Use the following data for a firm's output at various levels of employment (L) to calculate: a) its marginal physical product of labor (MPPL) schedule; (b) its (MPPL/MRCL) schedule, given a fixed wage (W = MRCL) of $25 per hour per worker. (c) Assuming that capital (K) is held constant at 2 machines and MPPK/MRCK = 10, what is the least-cost input-combination of labor and capital and how much output is produced with that set of resources?

Number of Workers (L) Output (Q)

1 100

2 300

3 600

4 850

5 1000

6 1100

8. Problem-solving question: Use the following data for a perfectly competitive firm and the profit-maximizing input-combination rule to identify how many workers the firm will employ to maximize profits.

Number of Workers (L) MRPL MRCL

1 $200 $30

2 150 30

3 125 30

4 100 30

5 75 30

6 50 30

7 30 30

8 10 30

9. Problem-solving question: Use the following data on a firm's total cost schedules to calculate its average variable cost, average fixed cost, average total cost, and marginal cost schedules.

Output Total Cost Total Variable Cost Total Fixed Cost

1 $2075.00 $ 75.00 $2000.00

2 2140.00 140.00 2000.00

3 2180.00 180.00 2000.00

4 2280.00 280.00 2000.00

5 2400.00 400.00 2000.00

10. Problem-solving exercises: (a) Use the arc-approximation formula to calculate the price-elasticity of demand coefficient of a firm's product demand between the (quantity, price) points of (100, $20) and (300, $10). (b) Calculate the cross-price elasticity of demand coefficient of a firm's product X, given that a 5% increase in the price of its close substitute, product Y, causes the quantity demand of product X to increase by 10%. c) Calculate the income-elasticity of demand coefficient for a product for which a 4% increase in consumers' income will increase the quantity demanded by 6%.

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#### Solution Summary

This solution provides detailed answers to 4 common managerial economics exam questions:

1. Using Marginal Revenue Product and Marginal Revenue Cost to determine the optimal combination of inputs.

2. Determining the number of workers a firm will hire to maximize profits.

3. Calculating a firm's AVC, AFC, ATC and MC

4. Calculating arc elasticity, cross-price elasticity, and income elasticity.

Managerial Economics

PROBLEM ONE

The R. J. Jones Company is a publisher of cowboy novels - novels about the great western experience, where men were men, horses were horses, and...well, you get the idea. The corporation has hired an economist to determine the demand for its product. After months of hard work and the submission of a REALLY large bill, the analyst tells the company that the demand for the firm's novels (Qx) is given by the following equation:

(Qx) = 12,000 - 5,000Px + 5I + 500Pc

where Px is the price charged for the novels, I is income per capita, and Pc is the price of books from competing publishers.

Using this information, the company managers want to:

A. Determine what effect a price increase would have on total revenues.

B. Evaluate how the sale of the novels would change during a period of rising incomes.

C. Assess the probable impact if competing publishers raise their prices.

Assume that the initial values of Px, I, and Pc are $5, $ 10,000, and $ 6, respectively.

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PROBLEM TWO

Given the following data set, list the point elasticity and the total revenue at each price point. Where is the price elastic, and where is it inelastic? Where is revenue maximized? What is the rational price point? Fully explain.

Price Quantity

$ 10 1

9 2

8 3

7 4

6 5

5 6

4 7

3 8

2 9

1 10

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PROBLEM THREE

The following is the production possibilities for a firm. At 0 labor units (strangely enough), there are 0 units produced. At 1 labor unit, there are 10,000 units produced, at 2 labor units, there are 25,000 units produced, at 3 there are 45,000, at 4 there are 60,000, at 5 there are 70,000, at 6 there are 75,000, at 7 there are 78,000, and at 8 there are 80,000. If the price of each unit produced is $ 3, and labor cost is 12,000 per unit, at what level should the firm produce?