Question

The market for computer flash drives is competitive. The marginal cost of producing flash drives (supply) is given by marginal cost = 50 + 3*Q and marginal benefit = 300 – 2*Q.

a. What are the predicted equilibrium P and Q in the market for flash drives?

b. Suppose the price somehow gets stuck at $100. Is there a shortage or surplus? If yes, which is greater, quantity supplied or demanded, and by how much (i.e. how much is the shortage or surplus)? Definition: a shortage is an amount by which quantity demanded exceeds quantity supplied and a surplus is the amount quantity supplied exceeds quantity demanded.

c. Answer the same questions as in 3b for a price of $300.

Answer 1

Marginal cost = 50 + 3*Q

Marginal benefit = 300 - 2*Q

(a) The predicted equilibrium P and Q in the market for flash drives is where Marginal cost = Marginal benefit. The marginal cost is equal to the supply curve and the marginal benefit is equal to the demand curve.

50 + 3*Q = 300 -2*Q

3Q + 2Q = 300 - 50

5Q = 250

Q = 50.

We get the price by substituting P in either the marginal cost or marginal benefit function. Substituting it in the marginal cost function,

MC = 50 + 3Q = 50 + 3(50) = 50 + 150 = $200 or, P = $200

So, the equilibrium P = $200, and the equilibrium Q = 50 units.

(b) If the price somehow gets stuck at $100, there would be a shortage of goods in the market. Lets see why.

Substituting P = $100 in marginal cost equation,

marginal cost = 50 + 3Q

100 = 50 + 3Q

3Q = 50

Q = 50/3 = 16.67 units. = 17 units

This is the quantity supplied.

Substituting P = $100 in marginal benefit equation,

marginal benefit = 300 - 2Q

100 = 300 - 2Q

200 = 2Q

Q = 100 units.

This is the quantity demanded.

We see that the quantity demanded, 100 is more than the quantity supplied, 17 units. So, there is a shortage.

(c) If the price is $300, there would be a surplus of goods in the market. Lets see why.

Substituting P = $300 in marginal cost equation,

marginal cost = 50 + 3Q

300 = 50 + 3Q

3Q = 250

Q = 250/3 = 83.33 units. = 83 units

This is the quantity supplied.

Substituting P = $300 in marginal benefit equation,

marginal benefit = 300 - 2Q

300 = 300 - 2Q

0 = 2Q

Q = 0 unit.

This is the quantity demanded.

We see that the quantity demanded is 0 whereas the quantity supplied, 83 units. So, there is a surplus.