Calculate the price elasticity of demand between 60 and 20 from the information on demand and supply in the…

Question

Calculate the price elasticity of demand between 60 and 20 from the information on demand and supply in the previous question.

ScanSolve AI Tutor · Accepted Answer

To solve these elasticity problems, we will use the midpoint formula for elasticity, which is:

E = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{X_2 - X_1}{(X_2 + X_1)/2}}

where $Q$ is quantity and $X$ is the relevant variable (price, price of related good, or income).

Calculate the Price Elasticity of Demand (PED)
The demand information is given by the equation $Q_d = 100 - P$ .
- Initial price P_1 = \60 $, so$ Q_1 = 100 - 60 = 40$ units.
- Final price P_2 = \20 $, so$ Q_2 = 100 - 20 = 80$ units.
Substitute these values into the midpoint formula:
$PED = \frac{\frac{80 - 40}{(80 + 40)/2}}{\frac{20 - 60}{(20 + 60)/2}}$ $PED = \frac{\frac{40}{120/2}}{\frac{-40}{80/2}}$ $PED = \frac{\frac{40}{60}}{\frac{-40}{40}}$ $PED = \frac{2/3}{-1}$ $PED = -\frac{2}{3} \approx -0.667$
The price elasticity of demand is $\boxed{-0.667}$ .
Calculate the Cross Elasticity of Demand (XED)
- Quantity of Good X: $Q_{x1} = 500$ units, $Q_{x2} = 350$ units.
- Price of Good Y: P_{y1} = \2.00 $,$ P_{y2} = $6.00$.
Substitute these values into the midpoint formula:
$XED = \frac{\frac{350 - 500}{(350 + 500)/2}}{\frac{6.00 - 2.00}{(6.00 + 2.00)/2}}$ $XED = \frac{\frac{-150}{850/2}}{\frac{4.00}{8.00/2}}$ $XED = \frac{\frac{-150}{425}}{\frac{4.00}{4.00}}$ $XED = \frac{-6/17}{1}$ $XED = -\frac{6}{17} \approx -0.353$
The cross elasticity of demand is $\boxed{-0.353}$ .
Calculate the Income Elasticity of Demand (YED)
- Quantity demanded: $Q_1 = 50$ units, $Q_2 = 45$ units.
- Income: I_1 = \200 $,$ I_2 = $400$.
Substitute these values into the midpoint formula:
$YED = \frac{\frac{45 - 50}{(45 + 50)/2}}{\frac{400 - 200}{(400 + 200)/2}}$ $YED = \frac{\frac{-5}{95/2}}{\frac{200}{600/2}}$ $YED = \frac{\frac{-5}{47.5}}{\frac{200}{300}}$ $YED = \frac{-2/19}{2/3}$ $YED = -\frac{2}{19} \times \frac{3}{2}$ $YED = -\frac{3}{19} \approx -0.158$
The income elasticity of demand is $\boxed{-0.158}$ .
Interpret the results
- Price Elasticity of Demand (PED): The absolute value of PED is $|-0.667| = 0.667$ . Since $|PED| < 1$ , the demand for this good is inelastic. This means that a change in price leads to a proportionally smaller change in the quantity demanded.
- Cross Elasticity of Demand (XED): The XED is $-0.353$ . Since the value is negative, Good X and Good Y are complementary goods. This indicates that an increase in the price of Good Y leads to a decrease in the demand for Good X.
- Income Elasticity of Demand (YED): The YED is $-0.158$ . Since the value is negative, this good is an inferior good. This means that as consumer income increases, the demand for this good decreases.

Calculate the price elasticity of demand between 60 and 20 from the information on demand and supply in the previous question.

Answer

Step-by-step solution

Calculate the Price Elasticity of Demand (PED)

Calculate the Cross Elasticity of Demand (XED)

Calculate the Income Elasticity of Demand (YED)

Interpret the results

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