Econ 172

HW 2 Due Friday Feb 3

Chapter 3

Questions: 1, 4, 12, 14

1. If the price rises by 2% and the quantity demanded falls by 3% the elasticity is 3%/2% = 1.5

4. Since the shares of consumers who have cable TV rises with income, the income elasticity is positive, so it is a normal good. From the numbers given, it does not look like it is a luxury good, however, so the income elasticity is probably between 0 and 1.

12. So 80% of the eating oranges come rom California. Food Lion said its prices for fresh oranges would rise by 20% to 30%, which was less than the 100% increase it had to pay for the oranges. Why? Clearly the supply curve for oranges shifted left. If demand for oranges is price elastic (a reasonable assumption, since there are lots of substitutes for Calfiornia oranges, such as Florida oranges), then a big increase in price would result in a huge decrease in quantity demanded. If supply is relatively inelastic in the short run (a reasonable assumption) and demand is elastic, then the seller bears most of the burden of the natural disaster (think of a natural disaster as similar to a tax increase and a tax increase will be borne mainly by the seller if these elasticity relationships hold).

14. Freshwater pearls are now much more close substitutes to saltwater pearls than they used to be. In the good old days, when saltwater pearls were not very good, the cross price elasticity was a very small negative number. That is, when the price of (lousy) freshwater pearls fell, there was only a very small decrease in the quantity demanded of (good quality) saltwater pearls. Today, freshwater pearls are much better quality and much better substitutes for saltwater pearls. So any decline in the price of freshwater pearls leads to a much larger decrease in the quantity demanded of saltwater pearls.

Hence, the cross price elasticity has risen.

Problems: 15, 18

15. The demand for coconut oil is Q = 1,200 – 9.5p + 16.2Pp + 0.2Y

P is the price of coconut oil, Pp is the price of palm oil. And Y is income

P = 45 cents Pp = 31 cents and Q = 1,275

What is the price elasticity of demand for coconut oil: E = %chQd/%chP = (dQ/dP) (P/Q)

dQ/dP = -9.5 P/Q = 45/1275

So price elasticity = .335

The cross price elasticity of demand Exy = %Ch Qdcoconut oil/%Ch Pp = dQ/dPp x Pp/Q

dQ/dPp = 16.2 Pp/Q = 31/1275 = .39

Note that this question is answered in the back of the book. If I had asked for Q16, as I should have, the income elasticity of demand is %ChQd/%ChY = dQ/dY x Y/Q

And dQ/dY = .2

Y/Q = Y/1275

Now, how to calculate Y:

Q = 1,275 = 1200 – (9.5)(45) + (16.2)(31) + 0.2Y = 1200 – 427.5 + 502.2 +.2Y

So 1275 = 1274.7 + .2Y so 0.3 = .2Y and Y = 1.5

So the income elasticity of demand is .2 x 1.5/1275 = .000235

18. Apple Cider Demand Q = 100 - p

Supply Q = ¼ p

Qd = Qs at 100- p = ¼ p so 5/4p = 100 and p = 400/5 = 80. And Q = 20

Q is in hundreds of thousands of bottles per day

Now put a tax per bottle of 20 cents. We need to write the supply curve with price as a function of quantity, so the pre tax supply curve is p = 4Q. With the tax, the price is now 20 + 4Q =pt (Pt is the price with the tax) which means that Q = pt/4 – 5

The new equilibrium is where pt/4 – 5 = 100 – pt. Solve and get 5/4pt =105 or pt = 84. This is the price with the tax. Consumers pay 84 cents and firms receive 64 cents. The new quantity is Q = 100 – 84 = 16

The tax revenues received (20 cents x 16) = $320,000 per day could be used to hire work crews to clean up the environment.

1) Which good would you expect to have a greater price elasticity: a gallon of gasoline sold at a specific gasoline station on Main Street in Phoenix, a gallon of gasoline sold in Phoenix, or a gallon of gasoline sold in Arizona? Why?

The price elasticity will be highest for the gasoline sold on Main Street in Phoenix since there are many substitutes such as gas away from Main Street. Gasoline in Arizona has fewer substitutes, unless you happen to be on the border of Arizona.

2) The price elasticity of demand for gasoline is estimated to be -0.2. Two million gallons are sold daily at a price of $1. Use this information to calculate a demand curve for gasoline assuming it is linear.

Ed = 0.2 This means dQ/dP (the slope) x P/Q = .2 We know P = 1 and Q =2 million. So dQ/dP x ½ = .2

dQ/dP = 0.4 So the equation of the demand curve is Q = a - .4P We know Q and P at one point on the demand curve so 2 = a - .4(1) and a = 2.4

Therefore the equation of the demand curve is Q = 2.4 - .4p and Q is in millions of gallons.