Question

Part 1: Short Answer Questions (10 points each) 1) The estimated Canadian processed pork demand and supply functions are as the follow- ings: Qp = 100-3 p + 3 p + 5 + 2 Y, Os = 100 + 6 - 8 PA where Q is the quantity in million kilograms (kg) of pork per year; p is the dollar price per kg, Po is the price of beef per kg, pe is the price of chicken per kg, P, is the price of hogs per kg, and Y is the average income in thousand dollars. Suppose that po = $8.00 per kg, pe = $6.00 per kg, Pi = $4 per kg, and Y = $11. Answer the following questions. Note that you need to show your calculations and explain your results to receive full credit!) a) Assuming ceteris paribus, calculate price elasticity of supply and demand at the equilib- rium price and quantity under the conditions stated in above and explain your results. Are the demand and supply at equilibrium elastic? Explain. b) Using the price elasticity of demand, calculate how much the price would have to rise for consumers to demand 28 fewer million kg than the equilibrium quantity? c) What is the income elasticity of demand at the market equilibrium quantity, where Y=S11? Is pork a normal good? Assuming all else unchanged, if the average income increases by 20%, what would be the expected change in the demand for pork? d) If the demand function Qp = 100-3 p +3 po + 5 pc + 2 Y) is then re-estimated using

Answer 1

a. At equilibrium Qs = Qd.

100 + 6P - 8Ph = 100 - 3P + 3Pb + 5Pc + 2Y

Plugging in all the values, we get,

100 + 6P- 8 * 4 = 100 - 3P + 3 * 8 + 5 * 6 + 2 * 11

68 + 6P = 176 - 3P

6P + 3P = 176 - 68

9P = 108

P = 108/9

P = $12

Q = 100 + 6 * 12 - 8 * 4 = 140 units.

PES = $\delta Qs/\delta P$ * P/Q

$\delta Qs/\delta P$ = 6

PES = 6 * 12/140 = 0.5142

PED = $\delta Qd/\delta P$ * P / Q

$\delta Qd/\delta P$ = -3

PED = -3 * 12/140

PED = - 0.2571

The absolute value of price elasticity of demand is less than one, this implies that the demand is inelastic that means the quantity demand will change by a lesser proportion than the change in price. The negative sign shows the inverse relation between the price and the demand.

The absolute value of price elasticity of supply is less than one, this implies that the supply is inelastic that means the quantity supplied will change by a lesser proportion than the change in price. The positive sign implies the positive relation between the price and the supply.

the demand and the supply at the equilibrium are inelatic.

b. to demand 28 fewer million kg than the equilibrium would be 140 - 28 = 112 units.

PED = $\Delta Q/\Delta P$ * P/Q

-0.2571 = (28)/(P - 12) * 12/140

-0.2571 = 2.4/(P - 12)

P - 12 = -2.4/0.2571

P - 12 = -9.3348

P = -9.3348 + 12

P = 2.70

Rise in price = 12 + 2.70 = $14.70

c. IED = $\Delta Q/\Delta Y$ * Y/Q

IED = 2 * 11000/140

IED = 157.142

Yes, pork is a normal good as the income rises, the demand for pork increases by a greater proportion.

157.142 = % change in demand/+20%

157.142 * 20% = % change in demand

% change in demand = 31.428

d. The coefficient of income will remain the same and there will be no change in the coefficient of income with just dollars instead of thousads of dollars.

However, the income elasticity of demand will change.

IED = $\frac{d(100-3P+3Pb+5Pc+2Y)}{dY}\ast \frac{Y}{Q}$

IED = 2 * 11/140

IED = 0.1571

Now the income elasticity is less than one. The value of income elasticity is affected with this change. Now pork becomes an inferior good.