Which Equation Can Be Used to Find the Value of B if Side a Measures 8.7 Cm?

Solutions

Homework I

1)� A vegetable fiber is traded in a competitive world market, and the world price is $9 per pound.� Unlimited quantities are bachelor for import into the United States at this toll.� The U.South. domestic supply and demand for various price levels are shown below.

Price	U.South. Supply	U.S. Demand
	(million lbs.)	(1000000 lbs.)
3	2	34
6	4	28
ix	6	22
12	8	sixteen
xv	10	10
18	12	4

a.� What is the equation for need?� What is the equation for supply?

The equation for need is of the form Q=a-bP.� Beginning find the slope, which is

� You can effigy this out by noticing that every time price increases by iii, quantity demanded falls by vi meg pounds.� Demand is now Q=a-2P. To find a, plug in whatever of the cost quantity demanded points from the tabular array:� Q=34=a-ii*three then that a=40 and demand is Q=twoscore-2P.

The equation for supply is of the form Q = c + dP .� Starting time discover the slope, which is

� You can figure this out past noticing that every time toll increases by 3, quantity supplied increases past 2 million pounds.� Supply is now �� To discover c plug in any of the price quantity supplied points from the tabular array:� �so that c=0 and supply is

b.� At a toll of $nine, what is the cost elasticity of demand?� What is it at cost of $12?

Elasticity of demand at P=9 is

Elasticity of need at P=12 is

c.� What is the cost elasticity of supply at $ix?� At $12?

Elasticity of supply at P=9 is

Elasticity of supply at P=12 is

d.� In a free marketplace, what will be the U.S. price and level of fiber imports?

With no restrictions on trade, world cost volition be the price in the United States , and then that P=$9.� At this price, the domestic supply is half-dozen one thousand thousand lbs., while the domestic demand is 22 million lbs. �Imports make up the deviation and are sixteen million lbs.

2.� Much of the demand for U.S. agricultural production has come from other countries.� In 1998, the total demand for wheat was Q = 3244 - 283P.� Of this, domestic need was Q_D = 1700 - 107P.� Domestic supply was Q_S = 1944 + 207P.� Suppose the export demand for wheat falls past 40 percent.

a .�������� U.S. farmers are concerned virtually this drop in export demand.� What happens to the costless market cost of wheat in the United States ?� Do the farmers have much reason to worry?

Given total demand, Q = 3244 - 283P, and domestic need, Q_d = 1700 - 107P, nosotros may subtract and determine export need, Q_eastward = 1544 - 176P.

The initial market equilibrium price is plant by setting full demand equal to supply:

3244 - 283P = 1944 + 207P, or

P = $2.65.

The best way to handle the 40 pct drop in consign demand is to assume that the export demand curve pivots downward and to the left around the vertical intercept then that at all prices demand decreases by twoscore percent, and the reservation price (the maximum price that the foreign land is willing to pay) does non change.� If you instead shifted the demand bend downwardly to the left in a parallel fashion the outcome on price and quantity volition be qualitatively the same, but will differ quantitatively.

The new export need is 0.6Q_e=0.6(1544-176P)=926.4-105.6P.� Graphically, export demand has pivoted inwards equally illustrated in figure 2.5a below.

Total demand becomes

Q_D = Q_d + 0.half dozenQ_e = 1700 - 107P + 926.iv-105.6P = 2626.4 - 212.6P.

Figure 2.5a

Equating total supply and total demand,

1944 + 207P = 2626.4 - 212.viP, or

P = $i.63,

which is a significant drop from the marketplace-clearing cost of $two.65 per bushel.� At this price, the marketplace-clearing quantity is 2280.65 million bushels. �Total acquirement has decreased from $6614.6 1000000 to $3709.0 one thousand thousand.� Most farmers would worry.

b.�������� Now suppose the U.Southward. regime wants to buy enough wheat each twelvemonth to raise the toll to $3.50 per bushel.� With this drop in export need, how much wheat would the government have to buy?� How much would this toll the government?

With a cost of $3.fifty, the market place is not in equilibrium.� Quantity demanded and supplied are

Q_D = 2626.4-212.6(3.5)=1882.3, and�

Q_S = 1944 + 207(3.5) = 2668.v.�

Backlog supply is therefore 2668.5-1882.3=786.2 million bushels.� The government must buy this amount to support a price of $iii.v, and volition spend

$3.five(786.2 million) = $2751.7 million per twelvemonth.

iii)� The rent command agency of New York City has constitute that aggregate demand is

Q_D = 160 - 8P.� Quantity is measured in tens of thousands of apartments.� Cost, the average monthly rental rate, is measured in hundreds of dollars.� The agency too noted that the increase in Q at lower P results from more three-person families coming into the city from Long Island and enervating apartments.� The city�s board of realtors acknowledges that this is a good demand estimate and has shown that supply is Q_S = 70 + viiP.

a.�������� If both the bureau and the lath are right about demand and supply, what is the free market place toll?� What is the change in city population if the agency sets a maximum average monthly rental of $300, and all those who cannot find an apartment leave the metropolis?

To observe the free market price for apartments, set supply equal to demand:

160 - 8P = 70 + 7P, or P = $600,

since price is measured in hundreds of dollars.� Substituting the equilibrium toll into either the need or supply equation to determine the equilibrium quantity:

Q_D = 160 - (8)(6) = 112

and

Q_S = 70 + (7)(6) = 112.

We find that at the rental charge per unit of $600, the quantity of apartments rented is ane,120,000.� If the rent control agency sets the rental charge per unit at $300, the quantity supplied would and so be 910,000 (Q_Southward = 70 + (7)(3) = 91), a decrease of 210,000 apartments from the free market equilibrium.� (Assuming three people per family per apartment, this would imply a loss of 630,000 people.)� At the $300 rental rate, the demand for apartments is one,360,000 units, and the resulting shortage is 450,000 units (1,360,000-910,000).� Notwithstanding, excess demand (supply shortages) and lower quantity demanded are not the same concepts.� The supply shortage ways that the market cannot accommodate the new people who would have been willing to move into the city at the new lower cost.� Therefore, the city population will only fall by 630,000, which is represented past the drib in the number of actual apartments from 1,120,000 (the old equilibrium value) to 910,000, or 210,000 apartments with 3 people each.�

b.�������� Suppose the bureau bows to the wishes of the board and sets a rental of $900 per month on all apartments to allow landlords a �fair� rate of return.� If 50 percent of any long-run increases in apartment offerings come up from new construction, how many apartments are constructed?

At a rental rate of $900, the supply of apartments would exist 70 + 7(9) = 133, or 1,330,000 units, which is an increase of 210,000 units over the gratis market equilibrium.� Therefore, (0.five)(210,000) = 105,000 units would exist constructed.� Note, nonetheless, that since demand is only 880,000 units, 450,000 units would go unrented.

4)� In 1998, Americans smoked 470 billion cigarettes, or 23.5 billion packs of cigarettes.� The average retail cost was $two per pack.� Statistical studies have shown that the price elasticity of demand is -0.four, and the price elasticity of supply is 0.5.� Using this data, derive linear need and supply curves for the cigarette market.�

Let the demand curve exist of the general form Q=a-bP and the supply curve be of the general form Q=c + dP , where a, b, c, and d are the constants that you have to discover from the information given in a higher place.� To begin, recall the formula for the price elasticity of demand

You are given information about the value of the elasticity, P, and Q, which means that you tin solve for the slope, which is b in the above formula for the demand bend.�

To find the constant a, substitute for Q, P, and b into the in a higher place formula and then that 23.five=a-4.vii*2 and a=32.9.� The equation for demand is therefore Q=32.nine-four.7P.� To find the supply curve, recall the formula for the elasticity of supply and follow the same method as above:

To discover the constant c, substitute for Q, P, and d into the above formula and so that 23.v=c+5.875*2 and c=xi.75.� The equation for supply is therefore Q=11.75+5.875P.

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Source: http://akdeniz.bilkent.edu.tr/courses/micro/solhw1.htm