Homework 3-
1. Suppose the market for corn in a country is described by the following demand and supply equations:
Demand: P = 100 - (1/2)Q
Supply: P = 10 + (13/10)Q
Use this information to answer the following set of questions.
a. What is the equilibrium price and quantity in this market? For your answers you may round to the nearest whole number.
b. What is the value of total revenue for farmers in this market?
Suppose the government institutes a price support in this market of $80 per unit of corn.
c. Given the price support, how many units of corn will consumers buy?
d. Given the price support, how many units of corn will the government buy?
e. Given the price support, what is the cost to the government of this program if storage costs are $10 per unit of corn stored?
f. Draw a diagram illustrating this price support program. Make sure you label your diagram clearly and completely.
Suppose the government cancels the price support program and, in its place, institutes a price guarantee program where the guaranteed price for corn is $80 per unit of corn.
g. Given the price guarantee, how many units of corn will consumers buy?
h. Given the price guarantee, what is the price per unit of corn that consumers will pay? What is the total expenditure on corn made by consumers?
i. Given the price guarantee, how many units of corn will the government purchase?
j. Given the price guarantee, what is the cost to the government of this program if storage costs are $10 per unit of corn stored?
k. Draw a diagram illustrating this price guarantee program. Make sure you label your diagram clearly and completely.
2. Suppose the market for candy bars can be described as follows:
- When the price of candy bars is $1.00 per candy bar, 500 candy bars are demanded. When the price of candy bars increases by 10%, the quantity of candy bars demanded falls by 20%. The demand curve for candy bars is linear.
- The supply curve for candy bars is linear and contains the points (Q, P) = (300, $.60) and (200, $.50).
a. What is the equation for the demand curve given the above information?
b. What is the equation for the supply curve given the above information?
c. What is the equilibrium price and quantity in the market for candy bars?
d. Suppose the government wants to institute an effective price ceiling in the market for candy bars. What must be true for this price ceiling to be effective?
e. Suppose the government wants to institute an effective price floor in the market for candy bars. What must be true for this price floor to be effective?
3. Suppose that the government of Zanzi decides that there is a need to reduce cigarette smoking in their country. The cigarette market in Zanzi can currently be described by the following demand and supply equations:
Demand for cigarettes: Q = 1125 - 12.5P
Supply of cigarettes: Q = 1100P - 1100
The government proposes implementing a quantity control of 500 units: this quantity control would limit the number of cigarettes that could be sold in Zanzi to exactly 500 units. The government has asked you to evaluate this program by answering the following series of questions.
a. Before implementing the quantity control, what is the equilibrium price and equilibrium quantity of cigarettes in Zanzi?
b. Before implementing the quantity control, what is the value of consumer surplus in the market for cigarettes in Zanzi?
c. Before implementing the quantity control, what is the value of producer surplus in the market for cigarettes in Zanzi?
d. Suppose the government implements the quantity control. What price must consumers pay in order to only demand 500 cigarettes in Zanzi?
e. Suppose the government implements the quantity control. What price must producers receive in order to only supply 500 cigarettes in Zanzi? (Round your answer to the nearest cent.)
f. Suppose the government implements the quantity control. What price will the government sell the right to sell a unit of cigarettes for in Zanzi if the government sets the quantity control at 500 cigarettes?
g. Suppose the government implements the quantity control. What is the value of consumer surplus with this program? What is the value of producer surplus with this program? What is the government's revenue from this program?
h. Suppose the government implements the quantity control. What is the deadweight loss due to this program?
4. Coba is a small, closed economy. Coba's domestic demand curve and domestic supply curve for coconuts is given by the following equations where Q is units of coconuts and P is the price per unit of coconuts:
Domestic Demand: P = 100 - (1/20)Q
Domestic Supply: P = (1/60)Q
a. Given the above information, what is the equilibrium price and quantity in the market for coconuts?
b. Calculate the value of consumer surplus, producer surplus, and total surplus in the market for coconuts in Coba if this market is closed to trade.
Suppose the world price per unit of coconuts is $10.
c. Coba opens its coconut market to trade. How many units of coconuts will be imported once this market is opened to trade?
d. Given that Coba has opened its coconut market to trade, calculate the value of consumer surplus with trade, producer surplus with trade, and total surplus with trade for Coba in this market.
e. Is trade in the coconut market beneficial to Coba? Explain your answer.
f. In Coba, who favors opening the coconut market to trade and who opposes opening the coconut market to trade? Explain your answer.
Coba responds to domestic producer concerns by implementing a tariff that results in 600 units of coconuts being imported.
g. Given the imposition of this tariff, what is the new tariff price?
h. Given the imposition of this tariff, what is the new consumer surplus with the tariff, producer surplus with the tariff, and license holder revenue from the tariff?
5. Consider the market for widgets in Westonia, a small closed economy whose domestic demand and supply curves for widgets are described by the following equations:
Domestic Demand: P = 10 - Q
Domestic Supply: P = 2 + (1/3)Q
where P is the price per unit of widgets and Q is units of widgets. You are also told that the world price of widgets is $3 per unit of widgets.
a. Suppose that Westonia opens the widget market to trade. Will Westonia import or export widgets? Fully explain your answer.
b. Suppose the government of Westonia imposes an import quota of 5 units of widgets. Describe the effect of this quota on the market for widgets in Westonia.
c. Suppose the import quota is set by the government of Westonia at 2 units of widgets. What will be the price of widgets in Westonia due to the imposition of this quota?
d. Given the import quota described in part (c), what is the deadweight loss associated with this quota?
6. Answer the next set of questions about various kinds of elasticity.
a. You are given a demand curve, P = 10 - Q, and asked to calculate the arc elasticity of demand between the quantities of 1 unit and 2 units. Show the general equation you plan to use before putting in numbers. Also indicate if price elasticity of demand is elastic, inelastic, or unit elastic given the value you calculated.
b. You are given a demand curve, P = 10 - Q, and asked to calculate the arc elasticity of demand between the quantities of 9 units and 8 units. Show the general equation you plan to use before putting in the numbers. Also, indicate if demand is elastic, inelastic, or unit elastic given the value you calculated.
c. You are given a demand curve, P = 10 - Q, and asked to calculate the point elasticity of demand when price is equal to $7. Show the general equation you plan to use before putting in numbers. Also, indicate if demand is elastic, inelastic, or unit elastic given the value you calculated.
d. Currently bus tickets in your town are $1 per bus ride. You know that the demand for bus rides in your town is linear and that at a price of $1 per bus ride 50,000 rides a year are demanded. You also know that for every $0.50 increase in the price of a bus ticket demand decreases by 10%. Your community's transportation board wishes to increase bus revenue and is considering changing the price of a bus ticket by $0.25. Should the price increase to $1.25 or decrease to $0.75 if increased revenues is the sole goal of the transportation board? Provide a full, detailed explanation of how you determined your answer.
7. Consider the market for soft drinks. You know that the demand curve in this market contains the points (Q, P) = (100,000, $1.00) and (50,000, $2.00). You also know that the demand curve is linear. The linear supply curve contains the points (Q, P) = (0, $0) and (50,000, $1). The government decides they want to decrease consumption of soft drinks from its current equilibrium level to 50,000 drinks. You are asked to analyze this situation and provide answers to the following questions.
a. How big an excise tax will the government need to implement in order to reduce consumption to 50,000drinks?
b. Given the above scenario, calculate the tax revenue the government will collect when they implement an excise tax that reduces consumption to 50,000 drinks.
c. What is the deadweight loss associated with this excise tax?