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Computation of the elasticity of demand

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I am having a hard time understanding how to solve the following two quantitative problems. I am supposed to be able to solve for this problem given any set of values. Please feel free to make those up. I am just hoping to understand how to solve this problem if and when it comes up.

See attachment.

Thanks in advance.

1. Own Price elasticity or cross-price elasticity. Given a table of the price(s) and quantities before the price rises, how do you compute the POINT (or ARC) elasticity of demand of a good as its price rises.


Solve this problem for each one of these forms:
-Own-Price elasticity by point method
-Own-Price elasticity by arc method
-Cross-Price elasticity by point method
-Cross-Price elasticity by arc method

For own-price elasticity, state whether the demand for this good is elastic or inelastic.

For cross-price elasticity, state whether the goods are substitutes or complements.

2. A table like the one below is given, plus a wage and a cost of capital. The problem is to fill in the BLANKS. Put formulas in the cells above the variable names. Do not enter formulas in cells with "///" in them.

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Solution Summary

Given a table of prices and quantities, the point and arc elasticities of demand are calculated.

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Computing elasticity of demand

Question 1. The demand equation for a certain brand of metal alloy audio cassette tape is: 100 x^2 + 9 p^2 = 3600, where x represents the number (in thousands) of ten-packs demanded each week when the unit price is $p. How fast is the quantity demanded increasing when the unit price per ten-pack is $14 and the selling price is dropping at the rate of 15 cents per ten-packs/week? [Hint: To find the value of x when p = 14, solve the equation 100 x^2 + 9 p^2 = 3600 for x when p = 14].

Question 2a. Suppose the quantity x of Super Titan radial tires made available each week in the marketplace is related to the unit-selling price by the equation: p - (x^2 / 2) = 48, where x is measured in units a thousand and p is in dollars. How fast is the weekly supply of Super Titan radial tires being introduced into the marketplace when x = 6, p = 66, and the price/tire is decreasing at the rate of $3/week?

Question 2b. The demand function for a certain brand of compact disc is given by the equation: p = - 0.01 x^2 - 0.2 x + 8, where p is the unit price in dollars and x is the quantity demanded each week measured in units of a thousand. Compute the elasticity of demand E(p), and determine whether demand is elastic, inelastic or unitary when x = 15.

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