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..........?
Price setting firm- it means imperfect competitive firm.
1. Profit maximizing price where MR = MC
MR = 32 - 2Q -- [ TR = P*Q = 32Q - Q2 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 - ( 62 + 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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