Economics 1Professor Curtis

Problem Set 2 KeyMarket Equilibrium and Disequilibrium, Applications and Welfare, Elasticity

6) ) Suppose that the market demand for pizza is given by Qd = 300-15P and the market supply for pizza is given by Qs = 10P-50 where P=price per pizza. SHOW YOUR WORK!a) In equilibrium, how many pizzas would be sold and at what price?

Set D=S and solve for P: 300-15P =10P-50350 =25PP* = $14Q* = 10(14)-50 =140-50=90

b) What would happen if suppliers set the price of pizza at $10? Be specific here about quantity demanded, quantity supplied, etc. if they are not equal. If there is a surplus or shortage at this price, calculate its size, and clearly state whether this is a surplus or shortage.

At P=$10: Qs=10(10)-50=50Qd=300-15(10) =150Shortage of 100 pizzas

c) Suppose the price of hamburgers, a substitute for pizza, doubles. This leads to a doubling of demand for pizza (at each price, consumers demand twice as much pizza as before). Write the equation for the new market demand for pizza.

Qd = 2(300-15P) = 600-30P

d) Find the new equilibrium price and quantity for pizza.

Set new D=S and solve for P: 600 –30P =10P – 50650 =40PP* = $16.25Q* = 10(16.25) –50 = 112.5 (or rounded to nearest whole pizza )

Note: P* and Q* increased, as we would predict with a doubling of demand!

*** Can you draw this – the original demand and supply and then the shift? This will NOT result in a parallel shift as we usually see (since that is algebraically a bit more challenging) but you will still see a clear market outcome if D “tilts” right (but the intercept does not change).

2) Use the diagram below to answer the following questions. SHOW YOUR WORK!

P

$14 S

11 8 5 2 D

8 16 Q (millions of meals per day)

a) Calculate total consumer surplus at a price of $8 and production of 16 million meals per day.

½ (14-8)16 = $48 million

b) For the same equilibrium, calculate total producer surplus.

48 + 48 = $96 million (consumer and producer surplus are both equal to $48m)

c) If price remained at $8 but production was cut to 8 million meals per day, calculate the following:

Producer surplus = ½ (8*3) + 8*3 = $36 mill

Consumer surplus = same as producer surplus = $36 mill

Deadweight loss from underproduction = ½ (3)(8)*2 = $24 mill

Note: sum of above equals total surplus in earlier problem, as it should

d) What would happen to your answers in c) if production was cut to 8 million meals per day, and the price rose to $11? Calculate the following:

Producer surplus = ½ (3*8)+(11-5)*8 = $60 mill.

Consumer surplus = ½ (14-11)*8 = $12 mill

Deadweight loss from underproduction = ½ (3)(8)*2 = $24 mill (same as in c) above)

*** Could your analysis in d) apply to an excise tax placed on the sale of meals? If the tax increased the price to $11, can you calculate the size of the tax, quantity sold, price received by sellers and tax revenue raised by this excise tax? How would CS/PS change from your answers in d)?

8) Suppose vacationers and business travelers have the following demand for airline tickets from NY to Boston.

Price Quantity Demand (Business) Quantity Demanded (Vacationer)$150 2,100 tickets 1,000 tickets200 2,000 800250 1,900 600300 1,800 400

a) As the price of tickets rises from $250 to $300, what is the price elasticity of demand for

(i) business travelers? Show your work, using the midpoint formula.

inelastic demand

(ii) vacationers? Show your work, using the midpoint formula.

elastic demand

b) Why might business travelers have a different elasticity from vacationers?

Business travelers often fly out of necessity, given their jobs, and have less flexibility in terms of how and when they travel than do vacationers; thus demand for business travelers is inelastic in comparison to vacationers.

c) If the goal of airline companies is to increase sales revenue from airline tickets, what pricing strategy should they follow? In other words, whose (business traveler/vacationer?) prices should increase and whose should decrease? Please include in your answer how these pricing policies relate to elasticity.

Airline companies should raise the prices of business travelers since their demand is inelastic (and thus as P increases, TR will also increase) but should decrease prices for vacationers since their demand is elastic (so decreasing P raises Q “a lot” and thus TR will also increase)

9) You have been hired to predict the effects of increasing the price of iTunes songs by 10 percent, from $.99 to $1.09. You are interested in the effects of the price hike on the number of songs downloaded legally from iTunes, the number of songs downloaded legally from other online music sources, the number of iPods sold,and the number of CDs sold in stores. Given the hypothetical elasticities in the following table, fill in the blanks. Recall that conventional practice for price elasticity of demand of a product uses the absolute value of the elasticity.

Product Price Elasticity or Cross Price Elasticity

Predicted Percent Change in Quantity Demanded (+ for increases/- for decreases)

iTunes songs 1.50 (absolute value) - 15%

Songs from other online stores +2.00 + 20% (substitutes)

iPod players -0.70 - 7% (complements)

CDs in stores +1.80 + 18% (substitutes)

B. Using the table from question 4), write a sentence for each “product” above to explain what your numbers (and the signs) in the upper right column mean. If you can tell by the sign of the elasticity measure that the goods are complements or substitutes, please state that in your sentence.

For example,1) (iTunes songs) When the price of iTunes songs rises by 10%, the quantity demanded of iTunes songs will fall by ___% and demand for iTunes songs in price elastic since PED>1.

2) (Songs from other online stores)

When the price of iTunes songs rises by 10%, the quantity demanded of songs from other online stores rises (moves in the same direction, hence the + sign) by 20% since these goods are substitutes.

3) (iPod players)

When the price of iTunes songs rises by 10%, the quantity demanded of iPod players falls (moves in the opposite direction, hence the - sign) by 7% since these goods are complements.

4) (CDs from stores)

When the price of iTunes songs rises by 10%, the quantity demanded of CDs from other stores rises (moves in the same direction, hence the + sign) by 20% since these goods are substitutes.

C. If consumer incomes increase and the income elasticity of demand (IED) for iTunes songs is +1.5, what does this tell us about iTunes songs?

A positive IED says that as consumer income’s increase, the quantity demanded of iTunes also increases; this positive relationship tells us that iTunes songs are normal goods.