Question

One convenient way to express the willingness-to-pay relationship between ice and quantity is to use the inverse demand function. In an inverse demand function the price consumers are willing to for sale. Suppose the inverse demand function (expressed in dollars) for a product is P = 80-q, and the marginal cost (in dollars) of producing it is MC = 2q, where P is the price of the product and q is the quantity demanded and/or suppli

a. How much would be supplied in a static efficient allocation?
b. pay is expressed as a function of the quantity available ed. What would be the magnitude of the net benefits in dollars?
c. Assume that the government imposes a price control at P 80/3. Find the producer and th e consumer surplus associated with the resulting allocation.
d. Show graphically and explain in detail why price controls (either a price ceiling or a e floor) will result in a decline of the net benefits to society. Be sure to identify the welfare loss (loss of producer and/or consumer surplus).

Answer 1

To find a static efficient allocation, set MC equal to P, resulting in a quantity of 20 and price of $60, with total net benefits of $900. A government-imposed price control at P = 80/3 creates a surplus or shortage problem, reducing producer and consumer surplus. Price controls result in a welfare loss, depicted as deadweight loss on a graph.

Step-by-step explanation:

To achieve a static efficient allocation, we must set the marginal cost (MC) equal to the inverse demand function (P). Thus, set MC = 2q equal to P = 80 - q. This gives us q = 20. At this quantity, the price would be P = 80 - q = 80 - 20 = $60.

Next, the magnitude of the net benefits (also called social surplus) is the sum of consumer surplus and producer surplus. Consumer surplus can be found by the area above the price and below the demand curve, while producer surplus is the area below the price and above the supply curve. At the efficient allocation, consumer surplus is the triangle with a base of q = 20 and a height of (90 - 60), so it's 0.5 * 20 * 30 = $300. Producer surplus is the triangle underneath the price with a base of q = 20 and a height of 60, so it's 0.5 * 20 * 60 = $600. Adding these gives the total net benefits of $900.

With a price control at P = 80/3, the quantity demanded would be more than the quantity supplied, leading to a shortage. Producer surplus is the area above the controlled price but below the MC curve until the shortage quantity, while consumer surplus is the area below the demand curve and above the controlled price until the shortage quantity. Both surpluses would be smaller than at the efficient allocation.

Price controls, including a price ceiling or floor, cause a decline in net benefits to society as they lead to a misallocation of resources, either excess demand or excess supply. This is illustrated by the deadweight loss on a supply and demand graph, where the area of welfare loss is shown as the area of consumer or producer surplus that is no longer available due to the price control.