Suppose the demand for good X has estimated to be: lnQxd = 10 - 4lnPx –...

Suppose the demand for good X has estimated to be:

lnQ_x^d = 10 - 4lnP_x – 2lnP_y – 4 lnM.

a. How can you tell that demand is downward sloping?

b. What is the cross-price elasticity of demand between good X and Y?

c. Are good X and Y substitutes or complements?

d. Is good X a normal or an inferior good?

e. If the price of good X increased by 2 percent, what would happen to the quantity demanded of good X?

Expert Solution

a. demand curve is downward sloping because coefficient of price for good x is negative showing that when price of x rises quantity of x will fall and vice versa.

b. cross price elasticity of demand between x and y= (dQx/dPy)*(Py/Qx). Now this being a log-log model, coefficient of variable Y will give cross price elasticity. So cross-price elasticity of demand between good X and Y= -2

c. relation between Qx and Py is negative showing as price of y rises, demand for x will fall. So, this means as price of y rises its demand would fall and demand for x would also fall. This shows x and y are complements. Also if cross-price elasticity of demand between good X and Y are negative this shows they are complements.

d. X is an inferior good because coefficient of M is negative showing if income rises, demand for x would fall.

e. price elasticity of x is -2 this means if price of good X increased by 2 percent, then

elasticity= %change in quantity/%change in price

So, -2= %change in quantity/ 2

Solving we get, %change in quantity= -4

So, quantity demanded will fall by 4%.

Rahul Sunny answered 1 year ago

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