Suppose the demand for lychees is given by the following equation: Qd =4000–100P+500PM ,
where P is the price of lychees and PM is the price of mangoes.
a) What happens to the demand for lychees when the price of mangoes goes up? Are lychees and mangoes substitutes or complements?
b) Graph the demand curve for lychees when PM = 2.
Now suppose that the quantity of lychees supplied is given by the following equation: Qs =1500P–60R, where R is the amount of rainfall.
c. On the same graph you drew for part b,graph the supply curve for lychees when R= 50. Label the equilibrium price and quantity with P* and Q* respectively.
d. Calculate the equilibrium price and quantity of lychees.
e. At the equilibrium values, calculate the price elasticity of demand and the price elasticity of supply. Is the demand for lychees elastic, unit elastic, or inelastic? Is the supply of lychees elastic, unit elastic, or inelastic?
f. At the equilibrium values, calculate the cross-price elasticity of demand for lychees with respect to the price of mangoes. What does the sign of this elasticity tell you about whether lychees and mangoes are substitutes or complements? (Hint: Check to make sure that your answer is consistent with your answer to part a.)