Question

Government believes that access to the Internet is essential in today’s society, and to bolster access, it is proposing subsidizing the purchase of mobile devices. The inverse demand for mobile devices is given by P = 500 – 0.1 Q D . The supply is given by P = 200 + 0.1 Q S . a. Solve for the equilibrium price and quantity in this market, and calculate producer and consumer surplus. b. Suppose the government offers a $100 per unit subsidy to sellers of mobile devices. Alter the equation for the inverse supply curve to reflect the subsidy. c. With the subsidy in place, how many mobile devices will be sold? What will the price paid by buyers be? The price received by sellers? d. What will the subsidy program cost the government? What will the net effect of the subsidy on total surplus in society be?

Answer 1

The inverse demand is P = 500 – 0.1Q and the supply function is P = 200 + 0.1Q

a) Equilibrium in the market occurs when demand equals supply

500 - 0.1Q = 200 + 0.1Q

300 = 0.2Q

Q = 1500 and P = 200 + 1500*0.1 = 350.

CS = 0.5*(Max price - current price)*current qty = 0.5*(500 - 350)*150 = 11250

PS = 0.5*(Current price - min price)*current qty = 0.5*(350 - 200)*150 = 11250

b. Suppose the government offers a $100 per unit subsidy to sellers of mobile devices. New supply is P = 200 + 0.1Q - 100 or P = 100 + 0.1Q

c. With the subsidy in place, the new quantity and prices are

500 - 0.1Q = 100 + 0.1Q

400 = 0.2Q

Q = 2000 mobile devices and price paid by buyers = 500 - 0.1*2000 = $300. Price received by seller = 200 + 0.1*2000 = $400.

d. The subsidy program cost the government an amount = subsidy * quantity purchased = 100*2000 = 200000

There is a deadweight loss on the society measured by = 0.5*(100)*(2000 - 1500) = 25000