1. Suppose that the linear market supply curve starts on the price axis at $8 per box, and that the linear market demand curve hits the price at $7 per box. Is there an equilibrium in this market? Explain your answer.
2. The U.S supply of orange juice comes from Florida and Brazil. What is the effect of a freeze that damages orange crops in Florida on the market price of orange juice in the U.S? Use a diagram with supply and demand curves to illustrate your answer.
3. Ethanol is made from corn. Ethanol production increased 5.5 times from 2000 to 2008. What effect does the use of corn in order to produce ethanol have on the equilibrium price of corn?
4. Suppose the demand function for movies by FIU students is Q^dFIU = 200 - P, while the demand function for everyone else in Miami is Q^dMIA = 200 - 5P. What is the total demand function for movies?
5. If the supply of corn by the U.S is Q^sUS = a+bP, and the supply of corn by the rest of the world is Q^sW=c+eP, what is the entire world supply?
6. Consider the single-good commodity market model which can be described, as we did in class, by the two equations:
Q^d = c - dP (c, d >0) [demand]
Q^s = -e + fP (e, f >0) [supply]
a) Solve for equilibrium price and quantity.
b) Determine the effect a change in d will have on the equilibrium price and on the equilibrium quantity.
c) Determine the effect a change in f will have on the the equilibrium price and on the equilibrium quantity.
d) Show that if a per-unit tax of T dollars is imposed on the market, it does not matter whether the tax is levied on the consumers or producers equilibrium quantity is the same.
7. In a 2005 study titled "estimated of the supply and demand elasticities of California commodities," green et al. estimated the supply and demand curves for California processed tomatoes, among other goods. The supply function estimated by the study is given by
Ln = 0.2 +0.55 ln P,
Where Q is the quantity of processing tomatoes in millions of tons per year, and P is the price in dollars per ton. The demand function estimated by the study is
Ln =2.6 - 0.2 ln P + 0.15 lnPt,
Where Pt is the price of tomato paste in dollars per ton. In 2002, Pt = 110.
a) Solve for the equilibrium price and quantity of processing tomatoes.
b) Determine how the equilibrium price and quantity of processing tomatoes change if the price of tomato paste, in 2003, fall by 10%.
c) Now, suppose that government imposes a price floor on processing tomatoes at $65 per ton, how many tons of processing tomatoes will be sold in the market?
8. Suppose that the demand for cigarettes in a hypothetical economy is given by Q^d =2000 - 200Pc, where Q^d is the number of packs of cigarettes demanded and Pc is the price per pack. The supply of cigarettes is Q^s = 200Pc, where Q^s is the number of packs of cigarettes supplied.
a) Assuming the market is competitive; find the equilibrium price and quantity of cigarette packs.
b) Now, assume that in an effort to reduce smoking, the government levies a per-unit tax of $2.00 per pack on consumers. What is the price received by producers? The price paid by the consumers? The new market quantity?
c) What is the tax incidence for consumers? For producers?
9. Given the demand function Q^d = aP^-b derive the price elasticity of demand (E).
10. Given the supply function Q^s = c + dP derive the price elasticity of supply.
11. Given the supply function Q^s =dP, is the price elasticity of supply elastic, inelastic, or unit-elastic.
12. Suppose that the demand function for gadgets, is given by
Q^d = 1200 - 9.5P +16.2Pw + 0.2Y,
Where Q^d is the quantity of gadgets demanded I thousands, P is the price of gadgets, Pw is the price of widgets, and Y is weekly consumer income. If initially P = .45, Pw = .31, and Q^d = 1275, calculate the following:
a) Price elasticity of demand;
b) Cross price elasticity of demand; and,
c) Income elasticity of demand.
13. Assume that in a hypothetical economy the demand function for widgets is given by D(P(T)) and the supply function is S(P(T) - T), where demand depends on price, which in turn depends on the specific tax value, and supply depends on the price minus and the value of the tax.
a) Derive consumer incidence in terms of demand and supply elasticities.
b) Derive producer incidence in terms of demand and supply elasticities.
c) Show that as the supply curve becomes perfectly elastic, the entire incidence of the tax falls on consumers.