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Homework answers / question archive / In a market the inverse demand function is given by P = 180 – 0,5Q
In a market the inverse demand function is given by P = 180 – 0,5Q. Unit production cost is TL 40 and does not vary with the amount of goods produced. Assume that there are no other costs associated with production of this good.
a) Find the market equilibrium (equilibrium Q and P) if this market is perfectly competitive. Also compute the social welfare. (show all steps of your calculations) (10 p)
b) Find the market equilibrium (equilibrium Q and P) if this market is monopolistic. Also compute the social welfare. (show all steps of your calculations) (10 p)
c) Calculate the deadweight loss due to monopoly. Discuss what measures could be taken to eliminate the deadweight loss due to monopoly. (10 p)
2.) Briefly discuss equilibrium in perfectly competitive markets. Explain why the supply curve in perfectly competitive markets is parallel to the quantity axis in long run while it can be positively sloped only in the short run. (use graphs to support your explanations) (10 p)
The inverse demand function is given as P=180-0.5Q where P and Q represent the price and quantity of the output and the unit production cost is constant at 40 implying that the marginal cost of production or MC is constant at 40. Now, based on the profit-maximizing condition of a competitive firm, the competitive firm would produce the quantity of output which corresponds to the equality between the price and the marginal cost of production.
Therefore, based on the profit-maximizing condition of a competitive firm, it can be stated:-
P=MC
180-O.5Q=40
-0.5Q=-180+40
-0.5Q=-140
Q=-140/-0.5
Q*=280
Hence, the profit-maximizing output produced by a competitive firm would be 280 units, in this case.
Now, plugging the value of Q* into the inverse demand function, we get:-
P=180-0.5Q
P=180-0.5*(280)
P=180-140
P*=40
Thus, the profit-maximizing price charged by the competitive firm would be 40.
Now, when the Q is 0, the price that the consumers are willing to pay would be:-
P=180-0.5Q
P=180-0.5*(0)
P=180
Therefore, the consumer surplus in the competitive market, in this case, would be=0.5*(280-0)*(180-40)=140*140=19,600, and the producer surplus in the market be 0 since the marginal cost is constant and the price is equal to the marginal cost of production assuming a perfectly competitive market in this instance. Therefore, the total social welfare or total surplus in the market would be 19,600.
b) Now, the total revenue of production or TR would be=P*Q=(180-0.5Q)*Q=180Q-0.5Q^2 and the marginal revenue of production or MR=dTR/dQ=180-Q. Based on the profit-maximizing condition of the monopoly firm, it would produce the quantity of output which corresponds to the equality between the MC and MR.
Therefore, based on the profit-maximizing condition of the monopoly firm, it can be stated:-
MR=MC
180-Q=40
-Q=-180+40
-Q=-140
Q*=140
Hence, the profit-maximizing quantity produced by the monopoly firm would be 140 units.
Now, plugging the value of Q* into the inverse demand function, we can get:-
P=180-0.5Q
P=180-0.5*(140)
P=180-70
P*=110
Thus, the profit-maximizing price charged by the monopoly firm would be 110 in this instance.
Therefore, the consumer surplus, in this case=0.5*(180-110)*(140-0)=70*70=4900 and the producer surplus would be=110*140=15,400. Therefore, the total surplus or social welfare in the market would be=(15,400+4900)=20,300
c) The deadweight loss created in the monopoly market in this instance=0.5*(110-40)*(280-140)=35*140=4900. One of the government or administrative measures to remove or eliminate the deadweight loss in the monopoly market would be to mandate the monopoly firm or producers to produce its output level corresponding to the equality between the marginal cost of production and the market price of the concerned good or service. However, this would reduce the total revenue of the monopoly and the producer surplus as well as shown in part a) and b) of the answer. Now, in order to compensate for the loss in revenue and the overall producer surplus in the monopoly market, the government can perhaps subsidize the production of the concerned good or service in order to encourage the monopoly firm or producer to continue its production and maintain the monopoly profit level. Alternatively, the government can also enforce or impose a price ceiling in the monopoly by setting the market price of the good or service equivalent or identical to the marginal cost of production which would subsequently raise and safeguard the economic welfare of the consumers as this would also remove or eliminate the deadweight loss generated in the monopoly market.
2) As derived in part a) of the answer, the profit-maximizing output and price in the perfectly competitive market is determined by the equality between the market price of the concerned good or service and the marginal cost of production by the firms or producers. This essentially implies that as the firms in a perfectly competitive market are price takers, they do not have any control over the good or service price implying that the price and marginal revenue of production are identical in any competitive market. Now, the firms would continue to produce the output until the marginal cost of production is equal to the good or service price or the marginal revenue of production as that particular point the total or overall profit of the perfectly competitive firms or producers are maximized and the output level that corresponds to this equality or condition is considered as the equilibrium quantity of output in the competitive market. Since all the firms in a competitive market are price takers, they all follow the same principle in order to maximize their respective profit level.
Figure-1 in the document attached below illustrates the cost and revenue structure and the supply curve of a perfectly competitive firm in the short-run. The y and the x axes in figure-1 represent the price or P and the quantity of output or Q respectively. The MC, ATC, AVC, and AR/MR curves in the figure denote the marginal cost, average total cost, average variable cost, and the average revenue/marginal revenue curves respectively. The profit-maximizing price and the quantity of output in the competitive market are denoted as P* and Q* respectively corresponding to the intersection between the AR/MR or P and the MC curves. The short-run supply curve of the competitive firm is indicated by the region of MC curve that is marked with arrows implying that the short-run supply of any competitive firm is the part of the MC curve that is above the AVC or the average variable cost. The short-run supply curve of a competitive firm is labeled as SRSC in the figure 1 or the short-run supply curve. The competitive firm would essentially produce the output throughout the pat of the MC curve that is above AVc implying that the short-run supply curve of any competitive firm is generally upward sloping signifying a positive relationship between the price of the concerned good or service and its quantity supplied by the firm in the market.
Now, figure-2 in the document attached below illustrates the long-run situation in a perfectly competitive market. The y and x axes in figure-2 represent the price or P nd the quantity of output or Q respectively. The long-run demand and supply curves are labeled as D and LRSC curves respectively in figure-2. The long-run equilibrium price and quantity of output are denoted as P* and Q* corresponding to the intersection between D and LRSC curves. Now, since the competitive firm is a price taker, the market price or P is equal or identical to the marginal revenue of production and the average revenue of production as well. Therefore, the profit-maximizing price charged by the competitive firm would be equal to its marginal and average revenue of production. Now, recall that based on the profit-maximizing condition of any competitive firm, a competitive firm would produce the final output which corresponds to the equality between the marginal cost of production and the price or P implying that the profit-maximizing price charged by the firm is also equal to the marginal cost of production. This would essentially imply that the long-run supply curve of a perfectly competitive firm would be parallel to the x-axes which represents the quantity of output or Q as shown in figure-2.
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