Question

In: Economics

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

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.

Solutions

Expert Solution

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


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