Question

This is a price setting firm problem.(show all work)

Demand Function: P=32-Q

Total Cost Function: C=Q²+8Q+4

Profit maximizing price is.....?

Profit maximizing quantity is......?

Profit is......?

Lerner Index Value is......?

Price Elasticity of Demand is......?

To maximize sales, this firm would change a price...... and sell a quantity of..........?

Answer #1

Price setting firm- it means imperfect competitive firm.

1. Profit maximizing price where MR = MC

MR = 32 - 2Q -- [ TR = P*Q = 32Q - Q^{2} so MR = 32
-2Q]

MC = 2Q + 8 from TC

MR = MC

32 - 2Q = 2Q + 8

4Q = 24

Q = 6

P = 32 - Q = 32-6 = 26

So Profit maximizing price is $26

2. Profit maximizing quantity is 6 units.

3. Profit = TR - TC

= 26*6 - ( 6^{2} + 8*6 + 4)

= 156 - 36 - 48 - 4

= $68

4. Lerner's index = (P - MC) / P

MC = 2Q + 8 = 12+ 8 = 20

L = (26 - 20) / 26 = 0.23

**first four part is done completely post the other two parts separately**

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