1. find out price elasticity of demand and supply for the following functions when (a) P=8 and (b) Q=6.
i. P= 40 – 0.5Q
ii. Q= -40 + 0.75P
iii. Q – P + 2 = 0
iv. 2P + 0.2Q = 40
v. P = 20 – 2Q
vi. 4P + 4Q = 64
2. (i) When the demand function is 2Q – 24 + 3P = 0, find the marginal revenue when Q=3.
(ii) Given the demand function 0.1Q – 10 +0.2P + 0.02P2 =0, Compute the price elasticity of demand when P = 10.
(iii) If supply is related to the price the function P = 0.25Q + 10, find the price elasticity of supply when P = 20.
(iv) Given the demand function aQ + bP – k = 0, where a, b and k are positive constants, show that price elasticity of demand is minus one when MR = 0.
(v) when the demand is P = 20/(4 +Q), find out the price elasticity of demand when P = 4.
3. (i). A firm’s costs are 500 when output is 100. If the TC function is linear and fixed cost (FC) are 200, find the marginal cost when Q = 4, 5 and 6.
(ii). The following are estimates of TC and AC function for various firms. Compute the MC function in each case and say whether, or under what conditions, the MC function is economically meaningful.
(a). AC = 20/Q + 3 + 0.5Q
(b). AC – 2 = 100/Q + 0.2Q2 = Q3
(c). TC – 100 – 2Q + 2Q2 = Q3
(d). A.AC = a + bQ – cQ2 + gQ3
Where a, b and c are constants.
Given the MC when Q = 4 for (a), (b) and (c).
4. The following are AC and TC functions for various firms
(i). AC = 140/Q + 20
(ii) AC – a/Q = k
(iii) TC – 10 =2Q + 0.1Q2
(iv) TC – k – βQ = cQ2
Where a, k, β and c are positive constants.
(a) Find the expression for the gradients of the AC functions
(b) For what values of Q will AC be decreasing?
(c) Which functions would give U-shaped AC curves?
5. The market demand function of a firm is given by
4P + Q – 16 = 0
And the AC function takes the form
AC = 4/Q + 2 – 0.3Q + 0.05Q2
Determine the Q which gives:
(a) Maximum revenue
(b) Minimum marginal costs,
(c) Maximum profit
Use second derivative test in each case.