Question

Suppose demand for crude oil is given by \\[ Q=-2,000 P+70,000 \\] where \(Q\) is the quantity of oil in thousands of barrels per year and \(P\) is the dollar price per barrel. Suppose also that there are 1,000 identical small producers of crude oil, each with marginal costs given by \\[ M C=q+5 \\] where \(q\) is the output of the typical firm. a. Assuming each small oil producer acts as a price taker, calculate the market supply curve and the market equilibrium price and quantity. b. Suppose a practically infinite supply of crude oil is discovered in New Jersey by a wouldbe price leader and can be produced at a constant average and marginal cost of \(\$ 15\) per barrel. Assuming the supply behavior of the competitive fringe described in part (a) is not changed by this discovery, how much should the price leader produce in order to maximize profits? What price and quantity will now prevail in the market? c. Graph your results. Does consumer surplus increase as a result of the New Jersey oil discovery? How does consumer surplus after the discovery compare to what would exist if the New Jersey oil were supplied competitively?

Short answer

Question: Using the given demand and marginal cost functions, find the market supply curve, market equilibrium price and quantity, analyze the impact of a price leader with a constant marginal cost, and compare consumer surpluses. Demand function: Q = -2000P + 70000 Marginal cost function for each small producer: MC = q + 5 Solution (a): Individual firm supply curve and market equilibrium Step 1: Calculate the individual firm's supply curve from the marginal cost. P = MC P = q + 5 Step 2: Calculate the market supply curve by aggregating individual firm's supply curves. There are 1,000 identical small producers. So,  Qs = 1000q Step 3: Equate market demand and market supply to find the equilibrium price and quantity. Q = -2000P + 70000 Qs = 1000q Equating Q and Qs, and solving for P and q.

Step-by-step solution

Calculate the individual firm's supply curve from the marginal cost.

In order to determine the market supply curve, we first need to find the individual firm's supply curve from the marginal cost function \(MC=q+5\). Since firms are price takers, they will set their output level where price equals marginal cost (\(P=MC\)).

Calculate the market supply curve by aggregating individual firm's supply curves.

There are 1,000 identical small producers. So, to find the market supply curve (\(Q_s\)), we need to multiply the individual firm's output level by the number of firms: \(Q_s=1000q\).

Equate market demand and market supply to find the equilibrium price and quantity.

To find the market equilibrium, we will equate the demand function \(Q=-2000P+70000\) with the supply function \(Q_s=1000q\). Then, we will solve for the equilibrium price, \(P^*\), and corresponding quantity, \(Q^*\). For part (b):

Determine the price setter's monopoly price and quantity.

With an infinite supply of crude oil at a constant average and marginal cost of \(15 per barrel, the price leader will act as a monopolist. Determine the price and corresponding quantity where the price leader's marginal cost (\)MC = 15\() is equal to the market demand's marginal revenue (\)MR$).

Calculate the market price and quantity.

Now that the price leader's monopoly price and quantity are determined, find the market price and quantity, considering the competitive fringe's supply behavior remains unchanged. For part (c):

Graph the market demand, market supply, and price leader's marginal cost.

Graph the initial market demand curve, the market supply curve, and the price leader's marginal cost curve on a single graph, and mark the initial equilibrium point.

Graph the new market price and quantity with the price leader.

On the same graph, identify the new equilibrium point, which indicates the new market price and quantity after the price leader enters the market with an infinite supply of crude oil at a constant marginal cost of $15 per barrel.

Analyze consumer surplus before and after the oil discovery.

Determine whether consumer surplus has increased or decreased as a result of the increased oil supply from New Jersey and compare it to the consumer surplus if the New Jersey oil were supplied competitively instead of being monopolized by a single price leader. The step-by-step solutions for each part will help the student in understanding the core principles of market equilibrium, demand curve, supply curve, and consumer surplus with a practical example.

Key concepts

Demand Curve

The demand curve is a fundamental concept in economics that represents the relationship between the price of a good and the quantity demanded by consumers. It usually slopes downward from left to right, indicating an inverse relationship between price and demand. In the given exercise, the demand curve for crude oil is expressed through the equation: \[Q = -2000P + 70000\].

This equation tells us that as the price per barrel of oil increases, the quantity demanded decreases and vice versa. Let's break down the expression:

• The term \(-2000P\) indicates that for each dollar increase in the price, demand decreases by 2,000 barrels.
• The constant term \(70000\) represents the quantity demanded when the price is zero, although this scenario is purely hypothetical as oil always has a cost.

Understanding this equation allows us to predict how changes in the market price will influence consumer behavior. It's crucial to note that any shift in the demand curve can be caused by factors other than the price, such as changes in consumer preferences or income levels.

Supply Curve

In economic terms, the supply curve shows the relationship between the price of a good and the amount that producers are willing to supply. It typically slopes upwards, indicating that as the price of a good increases, suppliers are more willing to offer more of it in the market. The exercise provides that each small producer of crude oil has a marginal cost described by \(MC = q + 5\), where \(q\) is the output of the firm.

For the market supply curve, which aggregates the supply from all producers, we consider that there are 1,000 identical firms. Thus, we first find the individual firm's supply curve by setting \(P = MC\).

• The firm supplies oil when \(P > 5\), at a quantity \(q\) that solves the equation \(P = q + 5\).
• Rearranging the expression, we find \(q = P - 5\). This is each firm's supply curve.

To find the market supply curve, we multiply the supply of a single firm by 1,000 (the number of firms): \[Q_s = 1000(P - 5)\].

This relationship shows how the total supply in the market increases with price, which is foundational in finding the market equilibrium together with the demand curve.

Consumer Surplus

Consumer surplus is an economic measure of consumer benefit, representing the difference between what consumers are willing to pay for a good versus what they actually pay. It's depicted as the area between the demand curve and the market price line up to the quantity purchased on a graph.

Let's explore how this applies to the given exercise. Initially, with the market in its natural state before New Jersey's discovery, consumer surplus can be found using the equilibrium price and quantity determined by where the original demand and supply curves intersect.

With the introduction of a new supplier from New Jersey offering crude oil at a constant marginal and average cost of \(15\) per barrel, a new price and quantity equilibrium are established. If the price set by this new, plentiful supply is lower than the original equilibrium, consumer surplus increases because consumers can purchase oil at a lower price and in greater quantities.

• The increased consumer surplus is the area that extends the previous surplus under the new lower price level and up to the new quantity.
• This reflects the benefit to consumers from the increased availability of oil at a lower price.

Understanding the changes in consumer surplus helps evaluate the consumer benefits from new developments in a market, such as technological advancements or resource discoveries, thereby illuminating the full impact beyond just the price changes.