Answer to Question #258641 in Microeconomics for Hini

Question

İf the supply curve is q = 3 + 1.5p, what is the producer surplus if the price is 12?

Answer 1

Producer surplus is the difference between the market price and the price at which the producers are willing to sell the product. It can be calculated as the area above the supply curve upto the market price and quantity.

The producer surplus is calculated as,

$Producer surplus=p^*×q^*−∫^{q*}_0P(q)dq$

The supply function can be written as

$q=3+1.5p\\1.5p=q−3\\p=\frac{q}{1.5}−2$

Therefore the producer surplus can be calculated as,

$Producer \space surplus=12×21−∫^{21}_0(\frac{q}{1.5}−2)dq\\=252−[\frac{q^2}{3}−2q]^{21}_0\\=252−(147−42)\\=147$

Therefore the producer surplus is 147 units.