1. Consider a vitamin supplement that is supplied by many different firms. The demand curve is 𝐷 = 16 − 3𝑝 and the supply curve is 𝑆 = −4 + 2𝑝. (a) Find the competitive equilibrium. (b)Compute the consumer surplus and producer surplus. (c)Scientists discover that a vegetable is rich in this vitamin and the vegetable is not expensive at all. As a result, the demand curve shifts to 𝐷 = 14 − 4𝑝. The supply curve remains the same. Find the competitive equilibrium after the scientific discovery. (d)Compute the consumer surplus and producer surplus after the scientific discovery. (e)After making the calculation that you just made, Consultant Bob finds that the social surplus decreases after the scientific discovery. Therefore, he concludes that the discovery creates a deadweight loss and is detrimental to the society. Evaluate this argument. (Limited to 200 words.)

(a) To find the competitive equilibrium, we set the demand curve equal to the supply curve and solve for p (price).

16 - 3p = -4 + 2p

This simplifies to 5p = 20, so p = 4.

Substitute p = 4 into either the demand or supply equation to find the quantity.

D = 16 - 3*4 = 4

So, the competitive equilibrium is at price 4 and quantity 4.

(b) Consumer surplus is the area between the demand curve and the price line up to the quantity sold. It is given by the formula 0.5*(base)*(height).

Base = 4 (quantity), height = 16 - 4 (maximum price - equilibrium price)

Consumer surplus = 0.5412 = 24

Producer surplus is the area between the supply curve and the price line up to the quantity sold.

Base = 4 (quantity), height = 4 - (-4) (equilibrium price - minimum price)

Producer surplus = 0.548 = 16

(c) With the new demand curve, set it equal to the supply curve and solve for p.

14 - 4p = -4 + 2p

This simplifies to 6p = 18, so p = 3.

Substitute p = 3 into either the new demand or supply equation to find the quantity.

D = 14 - 4*3 = 2

So, the new competitive equilibrium is at price 3 and quantity 2.

(d) Compute the new consumer and producer surplus in the same way as before.

Consumer surplus = 0.52(14 - 3) = 11

Producer surplus = 0.52(3 - (-4)) = 7

(e) The social surplus is the sum of the consumer and producer surplus. Before the discovery, the social surplus was 24 + 16 = 40. After the discovery, the social surplus is 11 + 7 = 18. So, the social surplus has decreased. However, this does not necessarily mean the discovery is detrimental to society. The decrease in social surplus represents a transfer of benefits from consumers and producers of the supplement to consumers of the vegetable. The discovery could also have other benefits not captured in this model, such as improved health from eating more vegetables. Therefore, it's not accurate to conclude that the discovery creates a deadweight loss and is detrimental to society based solely on the decrease in social surplus.