Reference no: EM13333061

1. Calculate 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, calculate 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), calculate 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. Calculate 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 will 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

Find the Q which gives:

(a) Maximum revenue

(b) Minimum marginal costs,

(c) Maximum profit

Use the second derivative test in each case.