Question

Part 1: Short Answer Questions (10 points each) 1) The estimated Canadian processed pork demand and supply functions are as the follow- ings: Q = 100-3 +3 p + 5 + 2Y, Os = 100 + 6 - 8 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, PA is the price of hogs per kg, and Y is the average income in thousand dollars. Suppose that ps = $8.00 per kg, pe- $6.00 per kg, P: -S4 per kg, and -S11 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 +3 + 5 + 2Y is then re-estimated using 2 A3.2.0 just dollars instead of thousand dollars i..e when income is measured in thousand dollars) what will be the effect on the coefficient for Y and the income elasticity at the market equi- librium, calculated in (c), with other conditions remaining the same? Calculate the income elasticity of demand and explain your results.

Answer 1

1. a. The values for price elasticity of demand and supply are found in detail and explained in the accompanying picture.

The value for price elasticity of demand will come out to be 0.25 and the value for price elasticity of supply will come out to be 0.51. This shows that our price elasticity of both demand and supply is inelastic which means that the percentage change in quantity with respect to change in quantity demanded and quantity supplied is not significant.

b. Detailed calculation in the accompanying picture.

Price should rise by $9.6 per million kg for demand to fall by 28 million kg.

c. Calculation in detail of the income elasticity of demand in the accompanying image.

Since income elasticity of demand comes out to be 0.157, we can say that pork is a normal good. This is because the value of income elasticity of demand is positive, which says that the demand for pork rises as the income rises. We can also say that pork is a necessity since its value lies between 0 and 1.

In part 2, Expected change in demand for pork is 3.14%.

d. The coefficient of Y should be 2/1000=0.002 so that the effect of change in units of measurement from thousand dollars to dollars is mitigated.

Income elasticity of demand will remain unchanged. (Explained in detail in the accompanying image).

The coefficient of our variable is calculated in such a way to measure the effect of change in our variable on the dependent variable. This also takes into account the unit of measurement of our variable. Thus the value of coefficient changes with the change in our unit of measurement. Since our coefficient takes into account the value of change in independent variable with respect to change in that respective dependent variable, our price elasticity of income did not change with the change in units of measurement due to the effect already mitigated by our coefficient.

DATE: a) we have do = 100- 3p t 3 pot Spot 24 ---- 2--100+ 6p - 8 pm - To find equilibrium price and quantity, we need to equate both the equations _"_bozos 100 - 3 p T 3P + 5 p + 24 = 10ot op- 8 pm It is geen that Pr = $8:00 per kg; Pe= $6.00 pregic --- $4 per kg Anche Y. $11, pel Putting there values in our elustion, we get 100-3p + 3 (8) + 5(6) + 2(11,000) = 16+ op 8 (M) 24 + 30 + 22, +32 - 99 - p = $12 per kg. so, equilibriun quantity 140 hr million kg To find price elasticity of denland au formula Lisi E= % change in a . - % change in P P a AP Now, we have the values for land s. However, to find e let us use a simple turk ho 100- 3p + 16 = 176-3p (using was gre When I changes by I in this function, q will change by -3. 8 AQ -3 - And Ed = 12 + €3) = -0.25 140 Similarly, Ege % change in Quantity supplied % chang in Price I {s: L. 148 = 12 + 6 = 0.51 AP) mallia = 68 +6p which shows when price changes by бетата ј а 'lom 9 € в (АР L

PgUp question] get Num LOCH we have Eda 1.102 - At equilibrium, b. 112 and a Mong It is given that 482-28 Blo, Ed ( 0.25 (from previous hitting there volues in , we (- 0.25 = 12 1728 - 140 AP - AP = L 2.4. 9.6 6) Q:25 Thus, the price should rise by million kg $ 9.6 per we know that Income closticity of demand = % change in Demand - % choys in Income Ey = AS Y - AY & we have do 100-3p+ 3 Pb + 5pc +24 Putting the values of all the prices, we get 0, 100 - 3"(12) + 3(8) + 5(6 + ana 11 8 + 2y for every increase in income by unit, quantity demanded will rise by 2 units. ooo, 48 = 2 - 4y Thus, Ey = 2 + 1 = 0.157 ____140 I Part 2 q this question says that % chaye in one is 20% with everything else uncharged 1 2 0 157 = 7. charm in Demand ) % change in Da 3.14% 20% -

oo Expected DATE change in Demand - 20% 0.157 = 3:14.7 sek 7 income is measured in dollars instead of thousand dollars our equation becomes --- 8-- 118 + 0.0024 - says that when our Income changes by / unit our demand changes by 0.002 units. LAS *Y lo - Eye 40.002) * 14,000, 140 0.157