Question

1. After a careful statistical analysis, the Franklin Company concludes the demand function for its product is

    Q = 16,784 – 232.43P + 0.225M – 895.3P_R

Where Q is the quantity demanded of its product, P is the price of its product, P_Ris the price of its rival product, and M is consumers’ per capita disposable income. At present, P = $22.50, P_R = $12.50, and M = $43,499.      

a. What is the price elasticity of demand for the company’s product? Is the demand for the product elastic, inelastic, or unitary elastic? If the company decides to increase sales of its product by 10% through a price-change, what should they do to price – Increase? Decrease? By how much?

b. Is the company maximizing its sales revenue by charging $22.50? If not, what price should it charge to maximize its revenue?

c. What is the cross-price elasticity of demand of the company’s product with respect to its rival company’s product price? Explain how a 5% decrease in the price of the rival company’s product would affect the demand for this company’s product.

d. What is the income elasticity of demand of the product? Is the product a normal good or an inferior good? Explain how a 4% increase in disposable income affect the demand of the product.

Answer 1

Q = 16784 - 232.43 P + 0.225 M - 895.3PR

A) Therefore to increase quantity sold by 10% price has to reduce by 19.23% aa per the information given. Elasticity is -0.52 . This means for a given percentage change in price , percentage change in quantity will be almost half of that percentage change in price and since we have negative sign with it , this means the direction of chnage in two variables should be opposite. Hence the above answer is justified.

dp 59 elashcity of demand - lpë dp (-23.9.43) (22.5) At P- 22.5, PR: 18.5, M: 48,4901, = 10,150.35 Hence ep: (-232.43) (22.5) = 0.58 coupprox) 10,150.35 since elasticity in magnitude is less than 1, therefore it is inelastic demand. if company, decides to increase by 101. ie og 1100 10 then ez % age change ing = 10 S rage change inp sage change imp | is -10 = -0,28% Percentage change in P required 3 -0.52 0,82

B) Sales Revenue of the Company is = PQ = TR=

16784P - 232.43(P^2) + 0.225M×P -895.3(PR×P)

dTR/dP = 16784 -(232.43)(2P) + 0.225M - 895.3(PR) = 0

==>. 1588.925 = 464.86 P ==> P = 34.18

At P= 22.5 , TR = (22.5)(10150.35) = 228,382.88

At P = 34.18, Q= 7435.57 and TR = 254,147.7826

Hence Total revenue is not maximum at P = 22.5. But as per our revenue maximization exercise, it will be max at P = 34.18

C) cross price elasticity = (dQ/dPR) (PR/Q) =

(-895.3)(12.5)/10150.35 = -1.10

As per the similar formula for cross price elasticity as mentioned above in percentage terms we see that percentage change required in Q will be 5(-1.1) = - 5.5 %

Hence if PR increasex by 5% then Q wi decrease by 5.5%

D) income elasticity is = (dQ/dM)(M/Q)

= (0.225)(43499)/(10150.35) = 0.96

Since the effect of increase in income is to increase the quantity of the good purchased ( because of positive sign with elasticity) therefore it is normal good.

Similarly percentage change in Q when there's a 4% income increase is (4)(0.96) = 3.84% ( increase)