An estimated demand function of a hypothetical f 0.-100-2P, +0.75P, + 10M , wher
ID: 1130451 • Letter: A
Question
An estimated demand function of a hypothetical f 0.-100-2P, +0.75P, + 10M , where Px is the price of the firm's product, Py is the price of a related product and M is the consumers ' income. Required: i. Explain any two factors that determine price elasticity of demand for a product ii. Obtain own price elasticity of demand when Px 5, Py 4 and M 100, and i. If firm's marginal cost is Ksh. 15 per unit, what would be the firm's optimal output 2 marks) (4 marks) (4 marks) interpret your results price?Explanation / Answer
(i) Two determinants of price elasticity of demand are:
(a) Time period
In short run, demand is more inelastic and elasticity is low, since consumers cannot quickly switch to substitutes. But in longer run, demand becomes elastic as switching to substitutes become easier, and elasticity is higher.
(b) Nature of the good
For necessity items, demand is inelastic and elasticity is low. For luxury items, demand is relatively more elastic and elasticity is high.
(ii) Plugging in given values,
Q = 100 - (2 x 5) + (0.75 x 4) + (10 x 100)
Q = 100 - 10 + 3 + 1,000
Q = 1,093
Elasticity = (dQ/dPx) x (Px/Q) = - 2 x 5 / 1,093 = - 0.0091
It means that as price of good X rises (falls) by 1%, its quantity demanded falls (rises) by 0.0091%. Since absolute value of elasticity is less than 1, demand is inelastic.
(iii) With downward sloping demand curve, profit is maximized by equating Marginal revenue (MR) with MC.
Q = 100 - 2Px + (0.75 x 4) + (10 x 100)
Q = 100 - 2Px + 3 + 1,000
Q = 1,103 - 2Px
2Px = 1,103 - Q
Px = 551.5 - 0.5Q
Total revenue (TR) = Px x Q = 551.5Q - 0.5Q2
MR = dTR/dQ = 551.5 - Q
Equating MR and MC,
551.5 - Q = 15
Q = 536.5
Px = 551.5 - (0.5 x 536.5) = 551.5 - 268.25 = 283.25