Question

You are given the following information about the demand for and supply of widgets in the Republic of Xénïa. Answer the questions that follow. If you draw diagrams, use a ruler, label the diagrams completely, show demand choke price, demand intercept, supply choke price, supply intercept, etc. Do not use double columns or put rectangles or squares around your answers. Use “D” for demand and “S” for supply. Do not use Qd or Qs to label your diagrams. Although you do not have to draw your diagrams to scale, make them big enough so that I can read them.

Qd = 20,000 – 1,000P (demand); Qs = 2,000P – 10,000 (supply), where P = price per unit (in Xénïa dollars X$) and Q = quantity.

(1) Determine the equilibrium price (Pe) and equilibrium quantity (Qe).

(2) Draw a diagram to illustrate your answer. Label the diagram completely.

(3) Determine the consumer surplus (CS) and producer surplus (PS):

(i) CS

(ii) PS

(4) Suppose the government of Zénïa imposes a price ceiling of $8 per widget. What will be the effect of this government-imposed price ceiling on consumers and sellers/producers of widgets?

(i) Qd at P = X$8.00 per unit.

(ii) Qs at P = X$8.00 per unit.

(iii) Draw a diagram to illustrate your answer. Label your diagram completely.

(5) Assume that a black market does not form—that is, the effective price in the market is the price ceiling of X$8.00 per unit. Determine the following:

(i) CS

(ii) PS

(iii) Deadweight loss (DWL)

(6) Assume that a black market forms. Determine the following:

(i) draw a diagram to illustrate your work.

(ii) the black-market price and indicate it on the diagram.

(ii) CS

(iii) PS

(iv) DWL.

Answer 1

1) Equilibrium at where Qd=Qs

20,000-1000p=2000p-10,000

P=30,000/3000=10

Q=20,000-1000*10=10,000

2)

3) Consumer surplus=1/2*equilibrium Q*(willingness to pay- equilibrium price)

Inverse demand:P=20-0.001q

Willingness to pay=20

Consumer surplus=1/2*10,000*(20-10)=10,000*5=50,000

Producer surplus=1/2*equilibrium Q*(equilibrium price- minimum price at which seller willing to sell)

Inverse supply:p=5+0.0005Q

Minimum price at which seller willing to sell=5

Producer surplus=1/2*10,000*(10-5)=5000*5=25,000

4)i) Qd at p=8$,

Qd=20,000-1000*8=12,000

ii) Qs at p=8$

Qs=2000*8-10,000=6000

iii)