Demand & Supply, Elasticity and Market Intervention Problems

1. Given the following linear demand functions, mathematically prove that AB will have a smaller own-price point elasticity than CD at any given price (other than at the end points of the lines). AB & CD are parallel

2. Given the following straight line demand functions, mathematically prove that AB will have a smaller own-price point elastictity than CD at point X.

  1. Calculate the numerical value of the elasticity of supply at point X.
  1. (a) If the supply curve for fake tatoos is Qs = -10,000 + 5,000P and the demand curve is Qd = 40,000 - 2,000P, what will be the effect of a price ceiling of $5? Will the market be in equilibrium? If not, how much excess demand will there be at this ceiling price?

(b) Fake tattoos have fallen out of fashion recently, and the demand curve for fake tattoos is now Qd = 20,000 - 2,000P. What will be the effect of the $5 price ceiling now? Will the market be in equilibrium? If not, how much excess demand or excess supply will there be at the ceiling price?

  1. (a) Given the following demand and supply equations plot the demand and supply curves and solve for equilibrium price and equilibrium quantity.

QD = 189 – 2.25P

QS = 124 + 1.5P

  1. Consider the demand for and supply of beer during the summer months:

QD = 30 – 5P +0.01I –2R

Qs = -100 + 20P

Where, Q is measured in thousands of six packs, P is the price per six-pack in dollars, I is income, and R is the number of rainy days during the summer.

(a)If I=$20,000 and R=15 plot the demand and supply curves in P-Q space. What is the equilibrium price and the equilibrium quantity?

(b) If I = $20,000 and R =10, plot the new demand curve and find the new market equilibrium price and new equilibrium quantity.

  1. Goods X and Y are complements in production and complements in consumption. Given that the price of good Y rises, explain what happens to the equilibrium quantity of X and the equilibrium price of X as a result of this price increase in Y. Draw a demand and supply graph of the market for X.
  1. Starting from a position of equilibrium in the jeans market the expected future price of jeans increases. Explain with graphs of the jean market what the new equilibrium price and equilibrium quantity will be. Assume that jeans are a normal good. Your answer must contain a few brief words of explanation pertaining to directions of curve shifts and the final impact on equilibrium values of price and quantity.
  1. Given an inverse demand function facing a monopolist that is defined as P = p(Q) and marginal revenue is defined as . Use the following definition of own price elasticity to show that .
  1. Given a demand function of the form:

(where Qx = Quantity of good X, Px = Price of good X, A and K are positive real numbers). Mathematically prove that the Marginal Revenue function for this particular demand function can be written as follows:

if you are defining own price elasticity as . OR Prove that if you are defining own price elasticity as .

For a firm facing the above demand function would raising prices in the top half of the demand curve lead to an increase in total revenue? Explain why or why not.

  1. Using demand & supply graphs illustrate two cases where the seller bears the entire burden of a per unit tax increase.
  1. The University of Lazy is located in the town of Lazy, CO. Currently, a typical student apartment rents for $300 a month and 15,000 apartments are rented. Assume that these are the market clearing values of P & Q. The University is considering expanding enrollments by lowering academic standards. A local economist estimates that at the current price and quantity, the price elasticity of demand for apartments is 1/4 and the price elasticity of supply is 1/2.

(a)What are the equations of demand and supply?

(b)Suppose there is an increase in the demand for apartments at the U of L. The new demand curve is given by Qd = 22,500 - 15P. What will the new equilibrium price and equilibrium quantity in this market be?

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