Answer to Question #147369 in Economics of Enterprise for Inaya Singh

Question

17. Given the following supply and demand equations

QD = 100 – 5P

QS = 10 + 5P

a) Determine the equilibrium price and quantity.

b) If the government sets a minimum price of $10 per unit, how many units would be supplied and how many would be demanded?

c) If the govt. sets a maximum price of $5 per unit, how many units would be supplied and how many would be demanded?

d) If the demand increases to

Q’D = 200 – 5P

Determine the new equilibrium price and quantity.

Answer 1

a) The equilibrium is at

$Q_d = Q_s \\ 100 – 5P = 10 + 5P \\ P=9 \\ Q = 100 - 5\times 9 = 55$

b)

$P=10 \\ Q_d=100-5 \times10 = 50 \\ Q_s=10+5 \times 10= 60$

The surplus = 60 - 50 = 10 units

It will maintain it by using law and order

c)

$P=5 \\ Q_d= 100 - 5\times 5 = 75 \\ Q_s=10+5 \times 5 = 35 \\$

The shortage =75 – 35 = 40 units

d) New equilibrium

$200 - 5P = 10+5P \\ P=19 \\ Q=10+5 \times 19 \\ Q =105$