Question

Suppose the demand curve for a product is given by Q = 500 − 2P + 4I, where I is average income measured in thousands of dollars. The supply curve is Q = 3P − 80. If I = 25, find the market-clearing price and quantity for the product. 

Answer 1

Let's first calculate the demand curve for a product if I=25:

$$Q_d=500-2P+4\cdot25=600-2P.$$

The market equilibrium occurs when $Q_d=Q_s$, then:

$$600-2P=3P-80,$$ $$680=5P,$$ $$P=\$136.$$

Therefore, the market-clearing price for the product is $136.

Finally, substituting $P$ into $Q_d$ we can find quantity for the product:

$$Q=600-2\cdot\$136=328.$$