Question

Isn’t this solution incorrect because the change in quantity is 100.not 48?

be widespread and prolonged shortages and even famine, which could result turmoil. A-head: 4.1 The price responsiveness of demand Learning Objective: The price elasticity of demand Type: Application 13 Suppose that the market demand for beef meat is given by Q -200-6P+ 2Y price of meat per kg and Y is the consumers' income. Suppose that consumers' income is £100. If the price of beef meat decreases from E10 to E8 per kg find the corresponding elasticity of demand. Now suppose that the price is fixed to E8 while consumers' income increases from £100 to £150, find the corresponding income elasticity of demand. Is beef meat a normal good? 130°#200-6p + 2Y when price E10 and income £100 200-60 + 200 340 When price - E8 and income remains at £100 0° = 200-48 + 200 " 352 Calculation for price elasticity of demand E - aQ*P/AP O (where P and Q are the original price and quantity. APandAQ are changes in price and quantity)

Answer 1

Q^D = 200 - 6P + 2Y

at P = 10 and Y = 100

Q = 200 - 6(10) + 2(100)

= 200 - 60 + 200

= 340

When P = 8 and Y = 100

Q = 200 - 6(8) + 2(100)  

= 200 - 48 + 200

= 352

Price elasticity of demand

Ed = - ($\Delta$Q$\times$P/$\Delta$P$\times$Q)

$\Delta$Q = 352 - 340

= 12

$\Delta$P = 8 -10

= -2  

Ed = -[12$\times$10/-2$\times$340]

= 120/680

= 12/68

= 0.176  

so Ed = 0.176 < 1 means inelastic demand

Now income elasticity of demand

E_Y  =  $\Delta$Q$\times$Y/$\Delta$Y$\times$Q

where Y = initial income and Q = initial quantity

At P = 8 and Y = 100

Q = 200 - 6(8) + 2(100)

= 352

now P = 8 Y = 150

Q = 200 - 6(8) + 2(150)

= 200 - 48 + 300

= 452

  $\Delta$Q = 452 - 352 = 100

  $\Delta$Y = 150 - 100 = 50

E_Y = 100$\times$100/50$\times$352

= 10000/17600

= 0.56

since income elasticity of demand is positive so beef is a normal good