Given the following supply and demand curve for goodcalculate the following: (a)

Question

Given the following supply and demand curve for goodcalculate the following: (a) Given Py, determine the equilibrium price and quantity for good r b Given ps and py, calculate the price elasticity of demand, the price elasticity of supply, and the cross price elasticity (c) Determine if the goods are demand complements or su bst itutes (d) Given py, determine which value of P makes the price elasticity of demand unitary elastic Unitary C or S? complements Complements 2p +1p (90-4p-3p 7 611 28 20 34 zli # 2 Complements 10 13 20+ 5p,-IPv 70-3px-2Pv 9 216 481.11 complements 11 19 6 24 41 Substitutes 36 76 91, _6Pv 100-3Pe + 2Ps 87|13 75 10+ 4p 1py 100-8p -2py 5 27 40 10+8p6Pv 100-2p,-IPv 7 4111 74 14 Substitutes Complements Complements 32 56 42 82

Explanation / Answer

Consider the given problem here the demand and the supply of good “X” are given below.

a).

=> “Qs=2Px+Py” and “Qd=90-4Px-3Py”. So, in equilibrium the demand must be equal to supply.

=> Qs=Qd, => 2*Px + Py = 90 - 4Px - 3Py, => 2*Px + 6 = 90 - 4Px – 3*6,

=> 2*Px + 6 = 72 - 4Px, => 6*Px = 66, => Px = 11. So, if the equilibrium price is “Px=11, => the equilibrium quantity demanded is given by, “Qx=28”.

b).

Now, given the demand curve, => “Qd = 90 - 4Px - 3Py”, => dQx/dPx = (-4). So, the price elasticity of demand is given by, “ed = [dQx/dPx]*(Px/Qx) = (-4)*(11/28) = (-11/7) = (-1.57).   

Now, from the supply curve, “dQs/dPx = 2”, => the elasticity of supply is given by as follows.

=> “es = [dQx/dPx]*(Px/Qx) = 2*(11/28) = 11/14 = 0.78.   

Similarly, given the demand curve, => “Qd = 90 - 4Px - 3Py”, => dQx/dPy = (-3). So, the cross price elasticity of demand is given by, “ec = [dQx/dPy]*(Py/Qx) = (-3)*(6/28) = (-9/14) = (-0.64).   

c).

Now, since the cross price elasticity of demand is negative, => these two goods are complement to each other.

d).

The price elasticity is given by, “ed = [dQx/dPx]*(Px/Qx) = (-4)*(Px/Qx), where “Qx=90-4*Px - 3*Py”.

=> ed = (-4Px)/(90-4Px -3*6) = (-4Px)/(72-4Px) = (-1), => (-4Px) = 4Px -72, => Px= 72/8 = 9.

So, here for “Px=9” the demand curve is unity elastic.

2).

a).

=> “Qs=10+5Px-4Py” and “Qd = 50-3Px-2Py”. So, in equilibrium the demand must be equal to supply, => Qs=Qd, => 10+5Px-4Py = 50-3Px-2Py, => 10+5Px-4*4 = 50-3Px-2*4, => 5Px-6 = 42-3Px => 5Px-6 = 42-3Px, => Px = 48/8 = 6

So, if the equilibrium price is “Px=6, => the equilibrium quantity demanded is given by, “Qx=24”.

b).

Now, given the demand curve, => “Qd =50-3Px-2Py”, => dQx/dPx = (-3). So, the price elasticity of demand is given by, “ed = [dQx/dPx]*(Px/Qx) = (-3)*(6/24) = (-3/4) = (-0.75).   

Now, from the supply curve, “dQs/dPx = 5”, => the elasticity of supply is given by as follows.

=> “es = [dQx/dPx]*(Px/Qx) = 5*(6/24) = 5/4 = 1.25.   

Similarly, given the demand curve, => “Qd = 50 - 3Px - 2Py”, => dQx/dPy = (-2). So, the cross price elasticity of demand is given by, “ec = [dQx/dPy]*(Py/Qx) = (-2)*(1/4) = (-0.5).   

c).

Now, since the cross price elasticity of demand is negative, => these two goods are complement to each other.

d).

The price elasticity is given by, “ed = [dQx/dPx]*(Px/Qx) = (-3)*(Px/Qx), where “Qx=50-3*Px - 2*Py”, => ed = (-3Px)/(50-3Px -2*4) = (-3Px)/(42-3Px) = (-1), => (-4Px) = 3Px -42, => Px= 42/6 = 7.

So, here for “Px=7” the demand curve is unity elastic.

3).

a).

Similarly, here also given the demand and the supply curve the equilibrium price and the quantity combination are given by as follows.

So, if the equilibrium price is “Px = 7, => the equilibrium quantity demanded is given by, “Qx = 39”. So, got these value by equating the “Qd” and “Qs” of good “X”.

b).

Now, given the demand curve, => “Qd = 70-3Px-2Py”, => dQx/dPx = (-3). So, the price elasticity of demand is given by, “ed = [dQx/dPx]*(Px/Qx) = (-3)*(7/39) = (-7/13) = (-0.179).   

Now, from the supply curve, “dQs/dPx = 2”, => the elasticity of supply is given by as follows.

=> “es = [dQx/dPx]*(Px/Qx) = 2*(7/39) = 14/39 = 0.36.   

Similarly, given the demand curve, => dQx/dPy = (-2). So, the cross price elasticity of demand is given by, “ec = [dQx/dPy]*(5/39) = (-2)*(5/39) = (-0.26).   

c).

Now, since the cross price elasticity of demand is negative, => these two goods are complement to each other.

d).

The price elasticity is given by, “ed = [dQx/dPx]*(Px/Qx) = (-3)*(Px/Qx), where “Qx=70-3*Px - 2*Py”, => ed = (-3Px)/(70-3Px -2*5) = (-3Px)/(60-3Px) = (-1), => (-3Px) = 3Px -60, => Px= 60/6 = 10.

So, here for “Px=10” the demand curve is unity elastic.

4).

a).

Similarly, here also given the demand and the supply curve the equilibrium price and the quantity combination are given by as follows.

So, if the equilibrium price is “Px = 11, => the equilibrium quantity demanded is given by, “Qx = 60”. So, got these value by equating the “Qd” and “Qs” of good “X”.

b).

Now, given the demand curve, => “Qd = 80-4Px+3Py”, => dQx/dPx = (-4). So, the price elasticity of demand is given by, “ed = [dQx/dPx]*(Px/Qx) = (-4)*(11/60) = (-11/15) = (-0.73).   

Now, from the supply curve, “dQs/dPx = 6”, => the elasticity of supply is given by as follows.

=> “es = [dQx/dPx]*(Px/Qx) = 6*(11/60) = 11/10 = 1.1 = es.   

Similarly, given the demand curve, => dQx/dPy = 3. So, the cross price elasticity of demand is given by, “ec = [dQx/dPy]*(8/60) = 3*(8/60) = 2/5 = 0.4.   

c).

Now, since the cross price elasticity of demand is positive, => these two goods are substitute to each other.

d).

The price elasticity is given by, “ed = [dQx/dPx]*(Px/Qx) = (-4)*(Px/Qx), where “Qx=80-4*Px + 3*Py”, => ed = (-4Px)/(80-4Px +3*8) = (-4Px)/(104-4Px) = (-1), => (-4Px) = 4Px -104, => Px= 104/8 = 13.

So, here for “Px=13” the demand curve is unity elastic.

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