Question

Question #4: Price Elasticity of Demand [14 Points]Suppose that the demand function for crab cakes is equal to 1200−=PQD(a) Using calculus calculate the price elasticity of demand when P = $20. [8 Points] (b) Is demand for crab cakes elastic, unit-elastic, or inelastic? Briefly explain [2 Points] (c) By how much should producers cut the price in order to sell 25% more crab cakes?

Question #5: Elasticity [22 Points] Consider the market for an Italian cookbook. Demand for the Italian cookbook is equal to QD = 3500 – 50P1 – 200P2Where P1 = price of the Italian cookbook and P2 = price of bottled olive oil The supply of the Italian cookbook is equal to QS = 150P1 - 500.(a) If P2 = $5, calculate the equilibrium price and quantity of Italian cookbooks. [2 Points] (b) If P2 = $5, derive the inverse demand curve. [2 Points] (c) Derive the inverse supply curve. [2 Points] (d) If P2 = $5, calculate the elasticity of demand (ED) and the elasticity of supply (ES) at equilibriumusing calculus. [6 Points] (e) Is the demand for Italian cookbooks elastic, unit-elastic, or inelastic? Briefly explain. [2 Points] (f) Is the supply for Italian cookbooks elastic, unit-elastic, or inelastic? Briefly explain. [2 Points] (g) At the equilibrium point, calculate the cross-price elasticity of demand for Italian cookbooks with respect to the price of olive oil using calculus. [4 Points] (h) Are Italian cookbooks and olive oil substitutes or complements? Briefly explain. [2 Points]

Question #6: Elasticity [12 Points] The demand for dog food, in pounds, is IPQD100124+−=where P is the price of dog food and I is income. Assume initially that P = 1 and I = 100. (a) Using calculus calculate the price elasticity of demand for dog food. [4 Points] (b) Using calculus calculate the income elasticity of demand for dog food. [4 Points] (c) Is dog food normal or inferior? Briefly explain your answer. [2 Points] (d) Is dog food a luxury good or a necessity? Briefly explain your answer. [2 Points]

Answer 1

5. a) Qd = 3500 - 50P1 - 200(5) = 3500 - 50P1 - 1000 = 2500 - 50P1

Qs = 150P1 - 500

Equilibrium condition; Qd = Qs

2500 - 50P1 = 150P1 - 500

3000 = 200P1

P1 = 15

Q = 150(15) - 500 = 2250 - 500

Q = 1750 units

b) QD = 3500 – 50P1 – 200P2

Q = 3500 - 50P1 - 200(5) = 3500 - 50P1 - 1000

Q = 2500 - 50P1

50P1 = 2500 - Q

P1 = (2500 - Q)/50

Inverse demand function; P1 = 50 - Q/50

c) QS = 150P1 - 500

150P1 = Q + 500

P1 = (Q + 500)/150

Inverse demand function; P1 = Q/150 + 3.33

d) P2 = 5

Q = 3500 - 50P1 - 200(5) = 3500 - 50P1 - 1000

Q = 2500 - 50P1

dQ/dP1 = - 50

Equilibrium points; P1 =15 and Q1 = 1750

Ed = P1/Q1 x dQ/dP1 = 15/1750 x - 50 = - 0.43

QS = 150P1 - 500

dQ/dP1 = 150

Es = P1/Q1 x dQ/dP1 = 15/1750 x 150 = 1.28

e) Demand is inelastic because Ed is less than 1.

f) Supply is elastic because Es is greater than 1.

g) Cross price Ed = % change in quantity demanded of Italian cookbook / % change in price of bottles olive oil

= P2/Q x dQ/dP2

QD = 3500 – 50P1 – 200P2

dQ/dP2 = - 200

P2 = 5

Q = 1750

Cross price Ed = 5/1750 x - 200 = - 0.57

h) Complementary goods because cross price elasticity is negative.

Increase in price of bottled olive oil decreases demand of Italian cookbook.