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Managerial Economics Questions: Arc Elasticity

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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.


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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Solution Preview

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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