Question

In: Economics

In the competitive market for sunglasses, the inverse demand is p= 35- (q/2) and the consumer...

In the competitive market for sunglasses, the inverse demand is p= 35- (q/2) and the consumer surplus in equilibrium is 344. What must be the price? (Round off answers to 2 decimal places). (I set the elasticity = -1 and got a price of 17.5 as the equilibrium price, but that is the wrong answer).

Expert Solution

Solution

The equilibrium price is 16.45.

Explanation

The equilibrium price can be calculated using the consumer surplus formula:

The formula of consumer surplus is:

To calculate the price, we need to solve for the consumer surplus:

The given consumer surplus is 344 (surplus is the triangle in the given figure).

The base and height can be calculated as follows:

The constatnt value in the inverse demand function p = 35 - (q/2) is the highest price that can be charged. Hence, as shown in the curve the starting point of demand curve is the point where price equals 35.

For the quantity, rearrange the equation as:

p = 35 - (q/2)

q/2 = 35 - p

q = 70 - 2p

Now,

The base for the consumer surplus formula will be: 35 - p

and, the height will be: 70 - 2p

Put these values in the consumer surplus formula:

p = 35 - 18.55

p = 16.45

Rahul Sunny answered 6 months ago

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