The Demand and Supply functions for pork in the textbook ex were:
Q^{D} = 171 - 20p_{b} + 3p_{c} + 2y
Q^{s} = 88 + 40_{p }
a. What is the inverse demand function for pork and how much would the price have to rise for consumers to want to buy 2 million fewer kg of pork per year.
b. If the price of beef, pb = $4/kg and the price of chicken pc = $3 1/3 kg and income
Y = 12.5 (in thousands of $), show how the equilibrium quantity of pork varies with income.
c. Show the effect of a decrease in income on the equilibrium using a well-labeled graph.
2. Due to a slight recession that lowered incomes, the 2002 market prices for last minute rentals of US beachfront properties were lower than usual.
a. How does a recession affect the demand curve and the supply curve for rental properties?
In answering the supply curve problem, consider the two options faced by owners of beach homes: staying in their vacation home themselves or renting them to others.
b. Use a supply-and-demand analysis to show the effect of decreased income on the price of
rental homes.
3. Suppose the market for Star Fruit is a competitive market, that every consumer in the market
has the same individual demand function:
q^{D} = 9 - 3p + p _{payaya} +2l
And that every firm in the market has the same individual supply function:
q^{S} = 1+ 2/3p - p _{fertillizer} -2p _{water}
a. If there are 100 consumers and 150 producers in the market, find the market demand and supply functions.
b. The price of papayas = $12 per bushel, $30 thousand (enter into function as 30), the price of fertilizer = $3 per liter, and the price of water = $4 per drum. Use the market supply and demand functions to solve for the equilibrium price and quantity of star fruit.
c. Find the price elasticises of market supply and demand at the equilibrium.
d. Is demand elastic or inelastic at the equilibrium price and quantity? What about supply?
e. Is star fruit a normal good? Find the income elasticity of demand at current prices.
f. Are papayas complements or substitutes?
4. Per Unit Sales Tax: For this problem, use the following supply and demand functions.
q^{S} = 9 + p
q^{d} = 114 -0.5p
a. Find the equilibrium price and quantity.
b. Now suppose there was a per unit tax of $2 collected from the sellers. prepare the new supply function.
c. Find the new equilibrium price and quantity.
d. What is the price that the buyers pay? What is the price the sellers receive?
e. What is the incidence of tax on buyers? describe using the idea of relative elasticities of Supply and Demand.
f. Label the effect of a tax on a S/D graph. In particular, show the area of the tax revenue.