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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.)

Question

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.)

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Solution

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

16 - 3p = -4 + 2p 5p = 20 p = 4

Substitute p = 4 into either the demand or supply equation to find q:

q = 16 - 3*4 = 4

So, the competitive equilibrium is p = 4, q = 4.

(b) Consumer surplus is the area above the price but below the demand curve. It is calculated as 0.5*(16-4)(4) = 24. Producer surplus is the area below the price but above the supply curve. It is calculated as 0.5(4-(-4))*(4) = 16.

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

14 - 4p = -4 + 2p 6p = 18 p = 3

Substitute p = 3 into the new demand equation to find q:

q = 14 - 4*3 = 2

So, the new competitive equilibrium is p = 3, q = 2.

(d) The new consumer surplus is 0.5*(14-3)(2) = 11. The new producer surplus is 0.5(3-(-4))*(2) = 7.

(e) Consultant Bob's argument is incorrect. The decrease in social surplus does not necessarily mean there is a deadweight loss or that the discovery is detrimental to society. The decrease in social surplus simply means that the total benefit to consumers and producers has decreased. However, this does not take into account the potential benefits to society from the increased consumption of the vegetable, such as improved health outcomes. Therefore, a comprehensive evaluation of the impact of the discovery on society should consider these additional factors.

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