Demand function : QD(P) = 56 - 1/2P Supply Function : Ps(Q)= 6Q (1) Compute the...

Demand function : Q^D(P) = 56 - 1/2P

Supply Function : P^s(Q)= 6Q

(1) Compute the market price and quantity in equilibrium.

(2) Compute the consumer and producer surplus in equilibrium.

In March 2020 an increase occurred, while the supply function did not change, the new reservation price for the demand function was found to be $200, while the slope of the demand function did not change.

(3) Compute the new market price and quantity in equilibrium as of March 2020.

(4) Compute the new consumer and producer surplus in equilibrium as of March 2020.

Solutions

Expert Solution

1. To solve for equilibrium quantity and price we can simply use P=6Q in the demand equation and obtain Q*=14 and then use this Q* in supply equation to obtain P*=84

2. Next we find maximum willingness to pay of buyer and find consumer surplus by using 1/2 × (max willingness to pay-equilibrium price) × equilibrium quantity.

Since supply equation starts from origin, minimum willingness to sell is at 0 and so we find producer surplus by using 1/2 × equilibrium price × equilibrium quantity

3. Next we use the new demand curve with the new reservation price. Use P=6Q in new demand equation and follow the same process we did in part 1.

4. The same method as used in part 2.

All calculations below-

Rahul Sunny answered 1 year ago

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