Calculate the price elasticity of demand and supply

Question

Assignment:

Question 1: Consider a competitive market for which the quantities demanded and supplied per year at various prices are

(a) Calculate the price elasticity of demand when the price is 25 and when the price is 30.

(b) Calculate the price elasticity of supply when the price is 25 and when the price is 30.

(c) Determine the equilibrium price and quantity

(d) Suppose the government sets a price ceiling of 20. Will there be a shortage? If yes, what is excess demand?

Question 2: Suppose that the demand and supply curve for wheat (measured in million bushels) in the US are given by Q_D(P)=3000-300P and Q_s(P)=1900+200P, respectively.

(a) Determine the equilibrium price and quantity of wheat.

(b) Suppose that because of a bad harvest in another country, the demand for US wheat is increased by 1000 units (i.e., 1 billion bushels) independent of the price P. Determine the new equilibrium price and quantity.

Question 3: Suppose you have the following information about the demand and supply of cotton in the U.S.:

(a) Determine the equations of the supply and demand curves.

(b) Determine the market equilibrium price and quantity.

(c) Now suppose that the US can import an arbitrary quantity of cotton at a price of 15 Dollars. How many units will the U.S. import?

Question 4: Suppose the demand for new and old apartments (together) is given by Q_D(P)=200- 0.1P. The supply curve for old apartments is Q_s^E(P)=30+0.03P. The supply curve for newly built apartments is Q_S^N(P)=20+0.02P.

(a) Determine the equilibrium price P, and how many apartments are built.

(b) Now suppose that the city government decides to control rents. That is, no landlord is allowed to ask for a rent that exceeds 600 Dollars. How many new apartments are being built now? Suppose that everyone who cannot find an apartment leaves the city. How many people will leave?

(c) Now suppose that instead of rent control, the government chooses to subsidize the building of new apartments. That is, the government pays 400 Dollars to landlords of any newly built apartments. Thus, the supply of new apartment is now given by 0.02(P+400). Determine the new equilibrium price P. Determine how many new apartments are built now and compute the total subsidy paid by the city government.

Question 5: Suppose that the price elasticity of demand for cigarettes is -0.2 and the price elasticity of supply is 0.5. The current price for a pack of cigarettes is 2 Dollars, and 500 billion packs of cigarettes are consumed annually.

(a) Determine the linear demand and supply curves for cigarettes.

(b) The government wants to reduce the consumption of cigarettes by imposing a tax of 2 Dollars per pack. Let P* be the new equilibrium price. Then, as a consequence of the tax, the buyer pays P*+2 Dollars for each pack of cigarettes. The seller still receives P* Dollars per pack. Determine

(i) The equilibrium price P*.

(ii) By how much does the tax reduce cigarette consumption.

(iii) The government's revenue from the cigarette tax.

(c) Now suppose that the government imposes a tax of 2 Dollars per unit on producers. Thus, if P is the new equilibrium price, then producers receive P-2, while consumers pay P Dollars per unit. Determine the following and compare your answrs to (b).

(i) The equilibrium price P*.

(ii) By how much does the tax reduce cigarette consumption.

(iii) The government's revenue from the cigarette tax.

Question 6: Suppose that the price elasticity of demand for copper is -1. The price elasticity of supply is 2. At a price of I Dollar per pound, Q=10 Million tons of copper are supplied and demanded.

(a) Determine the linear supply and the demand curve for copper.

(b) Suppose that demand for copper drops by 10 percent. Determine the percentage change of the equilibrium price and quantity.