Question

The demand for widgets (X) is given by the following equation:
Q_X = A P_X^{-0 .5} P_W P_Y^-1.25 P_Z^-0.25 I
where P_X is the price of widgets,
P_Y, P_W and P_Z are the prices of woozles, gadgets, and whatsits respectively, and I is income.
(A) The manufacturer of widgets is contemplating an increase in its price. Is it possible to know whether revenue will increase or decrease given that the initial price of widgets is not known? (2)
(B) By how much must the price of widgets change if income decreases by 4% and the goal is to keep QX constant? (2)
(C) By how much PX must change if the price of whatsits (PZ) increases by 2% and the goal is to keep QX
constant? (2)
(D) How are widgets and woozles related in consumption? (2)
(E) How are goods woozles and whatsits related in consumption? (2)

Answer 1

Now, 0.5 Price elasticity of demand for widgets 7. change in Ox 7. Change in Py 05 % change in ax = 0.5% -0.5 -0.5 % change in Px. -0.5 % change in Py = -0.5 % change in Px = 17 (11) » PX must instead decrease by IA to prevent fall and hence keep it When it before the increan en perice of whatsits (P2) constant was widges and wrozles; Cross Price slasticity of Demanos for widgets with respect to the price of 1.25 (PU) (ie Loefficient of log Py) Since woozles = -1.25 < As Py increases the demand for widgets falis tie. positive relationship, both complementary goods.