Answer to Question #117187 in Macroeconomics for Samkelo

Question

The accompanying table gives part of the supply schedule for personal computers in the United States.

Price of computer

Quantity of computers supplied

$1,100

12,000

$900

8,000



a. Calculate the price elasticity of supply when the price increases from $900 to $1,100 using the

midpoint method.

b. Suppose firms produce 1,000 more computers at any given price due to improved technology. As

price increases from $900 to $1,100, is the price elasticity of supply now greater than, less than, or the

same as it was in part a?

c. Suppose a longer time period under consideration means that the quantity supplied at any given

price is 20% higher than the figures given in the table. As price increases from $900 to $1,100, is the

price elasticity of supply now greater than, less than, or the same as it was in part a?

Answer 1

a.   Price elasticity of supply when price increases from $900 to $1100 using midpoint method

 

Percent change in quantity = $\frac{Q_2-Q_1}{(Q_2+Q_1)\div2}\times100$

                                     

                                            = $\frac{12000-8000}{(12000+8000)\div2}\times100$

= $\frac{4000}{10000}\times100$

 

                                             =40%

Percentage change in price = $\frac{P_2-P_1}{(P_2+P_1)\div2}\times100$

 

                                             =$\frac{1100-900}{(1100+900)\div2}\times100$

 

                                              = 20%

 

Therefore, price elasticity of supply is  40%/20% = 2

 

b.   The elasticity estimate would be lower. A price change from $900 to $1,100 is a 20% price change, just as in part a. When the quantity supplied changed from 8,000 to 12,000, that was a 40% change in the quantity supplied. Now that the quantity supplied at each price is higher by 1,000, the same price change would imply a change in the quantity supplied from 9,000 to 13,000,

 

 

                                              =$\frac{13000-9000}{(13000+9000)\div2}\times100$

                                              = $\frac{4000}{11000}\times100$

                                              = 36%

                                                     

           36% change using the midpoint method. The new price elasticity of supply is  

          36%/20% = 1.8, which is lower than in part a.

c.     The elasticity estimate would be unchanged. The price increase from $900 to $1,100 is a 20% increase, just as calculated in part a. But now that all quantities are 20% higher, the quantity supplied has increased from

20% increase of 12000 =2400 it will be 12000+2400 =14400

20% increase of 8000 =1600 thus 8000+1600 = 9600

        Using the midpoint method, this is an increase of  

=$\frac{14400-9600}{(14400+9600)\div2}\times100$

   =$\frac{4800}{12000}\times100$

= 40%

so that the price elasticity of supply is 40%/20% = 2

 Therefore, the price elasticity of supply is the same as in part a.