Question

Q_d = 7,000 – 10P

Q_s = -2,000 +  20P

a.   A. Find the equilibrium price and quantity, and graph your results, being sure to label everything relevant, including intercepts and slopes.  (20)

B. On your graph, identify the elastic and inelastic parts of the demand curve.  (10)

c.   C. Now suppose that the government imposes a $50 tax on suppliers of this product.  Find the new equilibrium price and quantity.  Show the effect of the tax in your graph.  (15)

d. D. Of the tax, consumers pay  $_________, and producers pay $____________.  (6)

e.     E. Calculate the price elasticity of demand and of supply at the original equilibrium point, and then explain WHY the tax is split in the way that you found above.  (14)

Answer 1

a) Set D=S

7000-10P = -2000+20P

7000+2000 = 20P+10P

9000 = 30P

P = 9000/30 = 300

Q = 7000-10*300 = 4000

B) The elastic portion ot the demand curve lies between P=700 and Equilibrium price

The inelastic portion of the demand curve lies between equilibrium price and P = 100

c) The tax will shift the supply curve up by the tax amount which decreased equilibrium quantity and increases price

The supply curve becomes: -2000+20(P-50) = -2000+20P-1000

Set D=S

7000-10P = -2000+20P+1000

7000+2000+1000 = 20P+10P

P = 10000/30 = 333

Q = 7000-10*333 = 3667

D) Of the tax, consumers pay = 333-300 = 33 and producers pay the remaining = 50-33 = 17