It has been estimated that the world demand for wheat can be represented by thefunction P = 80 - 2Q. It has been further found that the countries supplying thismarket have marginal cost curves which when summed together are given by theequation MC = 5 + Q
What price and output levels will prevail in the world market if a free marketsituation exists?
why "The sum of the individual MC curves of producers is the supply curve"?In monopoly they are lacking of supply curve??
Here the Total Revenue(TR)= P.Q =Q(80-2Q)=80Q-2Q2 ………………….(1)
We have theMR by differentiating equqtion in respect to Q.Therfore
d(P.Q)/dQ = 80-2.2.Q = 80-4Q
We know MC=5+Q……………….(2)
At the equilibrium, we have-
MR=MC
Hence, 80-4Q = 5+Q…………………(3)
Or -4Q+Q = 5-80
-3Q= -75
3Q =75
Q=75/3= 25
Again, putting the value of Q in equation (1),we have
25.P=80.25-2*25
=2000-50=1950
P=1950/25=78
The supply curve is the locus of the points representing the amount supplied by the producers at different prices. Under perfect competition the AR=MR curve is a horizontal straight line. So we have unique relationship between the quantity supplied with and the price. Thus under perfect competition the MC curve represent the supply curve the firm .We have the market supply curve by summing up the supply curves of the firms. But under monopoly such unique relationship is absent as the quantity supplied depend on the AR and MR and those curves are downward sloping. So supply curve is lacking under monopoly.
To determine the price and output levels that would prevail in a free market situation, we can use the given demand and marginal cost equations.
Given:
Demand function: P = 80 - 2Q
Marginal cost equation: MC = 5 + Q
In a free market, the market equilibrium occurs when the quantity supplied equals the quantity demanded. This is where the marginal revenue (MR) equals the marginal cost (MC). To find the equilibrium price and output levels, we need to set MR equal to MC and solve for Q.
First, let's find the marginal revenue (MR) by differentiating the total revenue equation (TR) with respect to Q:
TR = Q(80 - 2Q)
MR = d(TR)/dQ = 80 - 4Q
Next, we set MR equal to MC:
80 - 4Q = 5 + Q
Solving for Q:
-4Q - Q = 5 - 80
-5Q = -75
Q = -75 / -5
Q = 15
Now, substitute the value of Q back into the demand equation to find the price (P):
P = 80 - 2Q
P = 80 - 2(15)
P = 80 - 30
P = 50
Therefore, in a free market situation, the equilibrium price would be $50 and the equilibrium output level would be 15 units.
Regarding your question about the supply curve, in perfect competition, the sum of the individual marginal cost (MC) curves of all the producers represents the supply curve. This is because each producer will supply goods as long as the market price is higher than their individual marginal cost. The market supply curve is obtained by horizontally summing the individual supply curves of all the firms in the market.
In a monopoly, there is no unique relationship between price and quantity supplied because a monopolistic firm has market power and can set its own price. The quantity supplied by a monopolistic firm depends on the firm's marginal revenue (MR) and marginal cost (MC), and these curves can be downward sloping. As a result, there is no supply curve in a monopoly situation.