Question

Q5Using two goods X1 and X2 with their respective prices and , where both goods are normal goods. If the price of good X1 decreased from to , Using a clearly labeled diagram, explain and identify using either Hicksain approach or Slutsky approach the:-
i. Total change in demand for X
ii. Substitution effect
iii. Income effect
Q4Under 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 - 5 + . Find:
i. Revenue function (2 marks)
ii. The quantity produced at which profit will be maximum profit (6 marks)
iii. Maximum profit (2 marks)

Answer 1

Q5. The substitution effect is the economic understanding that as prices rise — or income decreases — consumers will replace more expensive items with less costly alternatives. Income effect: a parallel shape budget line is the movement that occurs when income change while the relative prices remain constant. This movement gives the income effect. This is the change of consumer income keeping the prices constant as illustrated in the equation below:
∆ xm = x1(p',m) − x1(p'm')
Q4. P = 6 per unit, C = 10 + 15Q - 5Q^2 + Q^3/3.
i. Revenue function TR = P*Q.
In equilibrium P = MR = MC = C' = 15 - 10Q + Q^2,
TR = P*Q = (15 - 10Q + Q^2)*Q = 15Q - 10Q^2 + Q^3
ii. The quantity produced at which profit will be maximum profit is when MR = MC = P = 6, so:
15 - 10Q + Q^2 = 6,
Q^2 - 10Q + 9 = 0,
Q1 = 9, Q2 = 1 - is not optimal.
iii. Maximum profit is:
TP(max) = TR - TC = 6*9 - (10 + 15*9 - 5*9^2 + 9^3/3) = 71.