EBK MICROECONOMICS
EBK MICROECONOMICS
5th Edition
ISBN: 9781118883228
Author: David
Publisher: YUZU
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Chapter 2, Problem 2.17P
To determine

(a)

To calculate the equilibrium price and quantity of golf balls, when R = 2 and T = 10.

Expert Solution
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Explanation of Solution

The following equations for demand and supply are given:

  Demand:Qd=902P2TSupply:Qs=9+5P2.5R

Substitute the values of R and T to solve for demand and supply equations in terms of price only as follows:

  Demand:Qd=902P2TQd=902P2(10)Qd=902P20Qd=702PSupply:Qs=9+5P2.5RQs=9+5P2.5(2)Qs=9+5P5Qs=14+5P

At equilibrium,

  Qd=Qs702P=14+5P7P=84P=$12

Substitute the value of price in any of the two equations to solve for equilibrium quantity as follows:

  Qd=702PQd=702($12)Qd=7024Q=46

To determine

(b)

To calculate the price elasticity of demand and price elasticity of supply at equilibrium values.

Expert Solution
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Explanation of Solution

The price elasticity of demand measures the degree of responsiveness of a change in the quantity demanded for a given change in the price level. It is calculated as follows:

  ed=d( Q d )dP×PQd=d( 702P)dP×P( 702P)=2×$1246=0.52

The price elasticity of demand at equilibrium values is '-0.52'.

The price elasticity of supply measures the degree of responsiveness of a change in the quantity supplied for a given change in the price level. It is calculated as follows:

  es=d( Q s )dP×PQs=d( 14+5P)dP×P( 14+5P)=+5×$1246=+1.30

The price elasticity of supply at equilibrium values is '+1.30'.

To determine

(c)

Cross-price elasticity of demand for golf balls with respect to the price of titanium.

Expert Solution
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Explanation of Solution

The cross-price elasticity of demand measures the degree of responsiveness of a change in the quantity demanded of a good for a given change in the price of some other good.

It is calculated as follows:

  εgolf,titanium=d( Q d )dPT×PTQd=d( 902P2T)dT×T( 902P2T)=2×10[902( 12)2( 10)]=2×1046=0.43

The negative sign indicates that titanium and golf balls are complements, i.e., when the price of titanium goes up, the demand for golf balls decreases.

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