Question

Suppose your firm is told that the demand function it faces from its market is given by

Q = 8 − 0.5

Its cost per unit is constant and equal to $1.5. Assume that it produces integer number of units (i.e. Q=0,1,2, 3...and so on).

(a) Describe in how you would use this demand function above to obtain your consumers’ marginal utility (or maximum willingness-to-pay) for each unit of your firm’s product.

(b) Construct a table showing the Price, Demand, Marginal Revenue and Marginal Cost schedule for the firm.

(c)Using Marginal Analysis, obtain the profit-maximizing linear price for the firm and calculate its profit level.

Answer 1

Sol:-

Inverse demand is P = 16 - 2Q. Marginal revenue is MR = 16 - 4Q

1) We have demand function P = 16 - 2Q and MR function and that MC = 1.5. Use different values of Q to find Demand , MR and MC

Quantity	Demand Price	Marginal revenue	Marginal cost
0	16	16
1	14	12	1.5
2	12	8	1.5
3	10	4	1.5
4	8	0	1.5
5	6	-4	1.5
6	4	-8	1.5
7	2	-12	1.5
8	0	-16	1.5

b) MR = MC

16 - 4Q = 1.5

Q* = 3.625 and price P = 16 - 2*3.625 = 8.75. Profit = (P - MC)*Q = (8.75 - 1.5)*3.625 = 26.28

c) Consumer surplus = 0.5*(max price - current price)*current qty = 0.5*(16 - 8.75)*3.625 = 13.14