Question

Consider the market for trinkets, where the demand and supply aregiven by the formulas:Demand :Quantity=100−PriceSupply :Quantity=−20+2∙Price (a) (10 points) Draw the demand and supply curves, and find the equilibriumprice and equilibrium quantity. (b) (10 points) Imagine that the government introduces a price cap of $30.Compare the consumer surplus before and after the cap is introduced.Are consumers better off or worse off? (c) (10 points) Imagine that now the price cap is reduced to $20. Comparethe consumer surplus after the new price cap with the consumer surpluswithout any cap. Are consumers better off or worse off?

please include an explanation of what steps you are taking to solve this problem thank you

Answer 1

Quantity Demanded: Q(d) = 100 - P

Quantity Supplied: Q(s) = -20 + 2P

a)

For demand curve:

When P =0, Q= 100. THus we have the horizontal intercept

When Q=0. P = 100. Thus we have the vertical intercept.

Joining both the points we have the demand curve.

Similarly for supply curve,

When P=0, Q = -20. This gives us the horizontal intercept.

When Q =0, P =10. This gives us the vertical intercept.

Joining both the points and extending it we get the supply curve.

At equilibrium , quantity demand equals qunaityt supplied, Thus Q(d) = Q(s)

100 - P = -20 + 2P

3P = 120

P = 40

Putting the value of P=40, we get

Q = 100 - 40

Q = 60

b)

Consumer surplus equals the area above the price line and below the demand curve.

Consumer Surplus(CS) before cap thus equals the area ABE=

CS before cap = area of triangle ABE = 1/2(100-40)*(60-0) = $1800

After the cap, Price equals $30. At P=30, Q(d) = 100 -30 = 70

the CS equals the area AGE

CS after cap = area of triangle AGE = 1/2(100-30)*(70-0) = $2450.

Thus the consumers are better off as CS after the cap is greater than CS before the cap.

c)

After the cap, Price equals $20. At P=20, Q(d) = 100 -20 = 80

CS after price cap of $20 equals the area of AIJ

CS after cap = area of triangle AIJ = 1/2(100-20)*(80-0) = $3200

Here also the consumers are better off as CS after the cap is greater than CS without a cap.

Please give a thumbs up if you found the answer helpful.