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Managerial Economics Questions: Arc Elasticity

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Facts:

Company XYZ Sells Drums Sets. At a price of $600 per set, they sold 500 Sets per month. The new manager decided that the company needed more revenue so she increased the price to $700 per set. However the company is now selling only 200 drum sets per month at the new price.

Questions:

1.What is the arc price elasticity for this product? Show work with results.

2.What do you recommend for the price of this product; stay at $700 or change higher or lower?

3.What additional information would be useful in the pricing decision?

4. What would be your recommendation for setting up a model to forecast future demand for this product?

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1.
P1 = $600
Q1 = 500
P2 = $700
Q2 = 200

The formula for arc elasticity uses the midpoint between the two known points on the Demand curve.

Ed = ((Q2-Q1)/(Q1+Q2)/2)/((P2-P1)/(P1+P2)/2)

Substituting the known ...

Solution Summary

This solution works out a concrete example of how to calculate the arc elasticity of demand for a product, and then to use that information to make pricing decisions.

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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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