Mr. Hassan’s demand function for rice is given by
X = 15 + M (10P) -1
Where X = amount of rice demanded, M = income of the consumer, P = price of rice.
Originally, the income of Mr. Hassan is $ 4,800 per month and the price of rice is $120/kg. If the price falls to $ 100/kg, calculate to total effect (TE), substitution effect (SE) and Income effect (IE) emanating from this change in price.
(a) Given the following monotonically transformed utility function faced by the consumer
U(X1X2) = X_1^0.5 X_2^0.5
The price of good X1 is P1 and the price of good X2 is P2. Derive the optimal demand (Marshallian demand) function for X1 and for X2.
Under a perfect competition the price as sh. 6 per unit has been determined. An individual firm has a total cost function given by C=10+15Q - 5Q^2+Q^3/3. Find:
i) Revenue function
ii)The quantity produced at which profit will be maximum profit
Question 1 Mr. Hassan’s demand function for rice is given by X = 15 + M (10P)^-1 M = $ 4,800 per month, P = $120/kg. If the price falls to $ 100/kg: 1) the total effect TE = X2 - X1 = 15 + 4800/(10*120) - 15 - 4800/(10*150) = 0.8 kg 2) substitution effect SE = Xh - X0 = 15 + (4800*150/120)/(10*150) - 15 - 4800/(10*120) = 0 kg 3) income effect IE = X1 - Xh = 15 + 4800/(10*150) - 15 - (4800*150/120)/(10*120) = 0.8 kg Question 2 (a) U(X1X2) = X1^0.5 X2^0.5 The price of good X1 is P1 and the price of good X2 is P2. Optimal demand (Marshallian demand) function for X1 and for X2 will be: X = (0.5I/P1, 0.5I/P2) Question 3 P = 6 per unit C=10+15Q - 5Q^2+Q^3/3. i) Revenue function is: TR = P*Q = 6Q ii) The quantity produced at which profit will be maximum profit is in the point, where marginal revenue equals marginal cost: MR = MC MR = TR' = 6 MC = C' = 15 - 10Q + Q^2 15 - 10Q + Q^2 = 6 Q^2 - 10Q + 9 = 0 Q1 = 9 units, Q2 = 1 unit (may not be profit maximizing). iii) Maximum profit is: TP1 = TR - TC = 6*1 - (10+15-5+1/3) = -$14.33 TP2 = TR - TC = 6*9 - (10 + 15*9 - 5*81 + 729/3) = 54 - 17 = $37