Problem 3: The demand curve for a product has the equation p =90 e 0.0028 q and

Question

Problem 3: The demand curve for a product has the equation

p=90e0.0028q

and the supply curve for this product has the equation

p=20e0.0029q,

where the price is in units of dollars/item.

Sketch the graphs of these curves.

What is the equilibrium quantity?

What is the equilibrium price?

What is the consumer surplus?

What is the producer surplus?

What is the total gain from trade for this product?



Suppose the price was artificially set to be $ 48.

What would be the demand at this artificial price?

What would be the supply at this artificial price?

Based on the two preceding answers, what quantity of the product would actually be bought and sold at this artificial price?

What would be the consumer surplus at this artifical price?

What would be the producer surplus at this artifical price?

What would be the total gain from trade at this artifical price?

Explanation / Answer

Problem 1

Equilibrium price = the corresponding price in the Y axis where demand and supply meets = $30

Equilibrium quantity = the corresponding quantity in the X axis where demand and supply meets = 120 units

Consumer surplus = ½ × Base × Height = ½ × 120 × (60 – 30) = $1,800

Producer surplus = ½ × Base × Height = ½ × 120 × (30 – 20) = $600

Gain = Consumer surplus + Producer surplus = $1,800 + $600 = $2,400

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