Answer to Question #72912 in Economics of Enterprise for Shamiah Martin

Question

Assume that demand and supply for a product over a period of time, respectively, are:

Qdx = 15 – 0.5Px and Qsx = 0.25Px – 3.



Calculate the equilibrium price and quantity. Clearly show your steps and manual calculations.

Quantify and discuss the impact of imposing a price of $20 per unit on the market, including the full economic price paid by consumers. Clearly show your steps and manual calculations.

If government should impose a $8 excise tax on the product, determine the new equilibrium price and quantity. Clearly show your steps and manual calculations. Graphically illustrate your answer.

Calculate the amount of tax revenue that government would earn with $8 excise tax. Clearly show your steps and manual calculations.

Answer 1

Qdx = 15 – 0.5Px, Qsx = 0.25Px – 3.
1) The equilibrium price and quantity are:
Qdx = Qsx,
15 – 0.5Px = 0.25Px – 3
0.75Px = 18,
Px = $24,
Qx = 15 - 0.5*24 = 3 units.
2) If the new price is $20, then Qdx = 15 - 0.5*20 = 5 units, Qsx = 0.25*20 - 3 = 2 units, so there will be a shortage of 3 units.
3) If government should impose a $8 excise tax on the product, then the new equilibrium price and quantity will be:
15 – 0.5(Px - 8) = 0.25Px – 3
0.75Px = 22,
Px = $29.33,
Qx = 15 - 0.5*29.33 = 0.33 units.
4) The amount of tax revenue that government would earn with $8 excise tax is:
0.33*8 = $2.64