The market demand for laptops (good X)

6. The market demand for laptops (good X) is given by: 

QX
D
= 1,200 – 0.4PX
1/2
– 4PY
1/2
+ 5I + AX 

Where QX
D
is the quantity demanded of laptops, PX is the price of a laptop, PY is the price of a 
smartphone, I is income, and AX is advertising expenditures on laptops. Suppose we know that 
PX is 200, PY is 40, I is 150, and AX is 10. 

A. Answer the following (using the demand determinant coefficients and calculus) 
(i) Is the law of demand satisfied? 
(ii) Are X and Y complements or substitutes? 
(iii) Is X a normal or inferior good? 
(iv) Is Y a normal or inferior good? 
B. Calculate a demand elasticity for each demand determinant. 
C. Are laptops a luxury or a necessity? 
D. Based on your elasticity value in Part B, would you characterize the advertising program 
as effective or not? Would you suggest that further advertising be undertaken? 

solution:
Part A: To calculate these answers, you need to take the proper derivatives. You cannot simply 
look at the coefficient as one might think. 
(i) Yes. QX/PX = – 0.2PX
-1/2
< 0 
(ii) Complements. QX/PY = – 2PY
-1/2
< 0 
(iii) Normal. QX/I = 5 > 0 
(iv) Unknown; Need QY/I 
Part B: To do these problems, you must find QX = 2,179.05. Then it is simply taking the proper 
derivative and formula, and plugging in. 
EQX,PX = (QX/PX)(PX/QX) = – 0.001298 
EQX,PY = – 0.0058 
EQX,I = 0.344 
EQX,A = 0.0046 
Part C: QX is a necessity since the income elasticity of demand is less than 1. 
Part D: It would seem to be very ineffective. Given that there will be costs incurred to finance 
the campaign, we can guess (but only guess) that the program is ineffective since EQX,A is so low. 

my question:
for part A) (ii) how to determine complements and substitution.
for part B) please explain in detail to me that why Qx=2179.05