1. Prove the proposition that the elasticity of demand at point A (with a price of P and quantity of C) is the length of the line segment 0P divided by the length of the line segment BP. (Hint, use the segments PA and OC and note that the length of PA and OC are equal. This is a short and elegant geometric proof, so if things seem to be getting complex, stop and restart.)
2. If the demand is given by Q = 10/P,
a. What is the Total Revenue when P= $5? When P= $2?
b. What is the elasticity of demand when P = $5? When P= $2?
c. What is the value of marginal revenue when P = $5? When P= $2?
3. On graph paper draw two straight-line demand curves on the same axes. The vertical axis intercepts of the two demand curves are identical, but the two curves have different slopes. For any price (that is less than the reservation price), what can you say about the relationship between the elasticity of demand at that price for one of the demands in comparison to the other demand?
4. If the Cross-Price elasticity of demand for good x responding to a price change in y approaches positive infinity, draw a representative set of indifference curves between goods x and y. What would a representative set of indifference curves look like if the cross price elasticity of demand approaches negative infinity?
Use this diagram to answer the questions below.
5. The equilibrium price is P0.
a. What is the area that represents the consumers’ surplus? _______________
b. What is the area that represents the sellers’ surplus? _______________
6. If an excise tax of (P+-P-) is imposed on buyers,
a. What is the area that represents the consumers’ surplus? _______________
b. What is the area that represents the sellers’ surplus _______________
c. What is the area that represents the government’s tax revenue? _______________
d. What is the area that represents the dead-weight loss? _______________
7. If a subsidy of (P+-P-) is given to sellers,
a. What is the area that represents the consumers’ surplus? _______________
b. What is the area that represents the sellers’ surplus? _______________
c. What is the area that represents the amount of the subsidy? _______________
d. What is the area that represents the dead-weight loss? _______________