Question
Part I 1.Question 1 (Perfect Competition) The local market for wheat is perfectly competitive. There are many potential firms (wheat farmers), each firm has a
Part I
1.Question 1 (Perfect Competition) The local market for wheat is perfectly competitive. There are many potential firms (wheat farmers), each firm has a cost function
C(q)=600+6q+4q for q>0, and C(0)=0.
a.Find the supply of each individual competitive firm.
b.Assume the market demand is Q= 1048-2P. The market is in a long run equilibrium with free entry and exit.
i.What is the equilibrium market price be?
ii.What quantity does each active firm produce?
iii.What is the total market quantity
iv.How many firms are active in this market?
c.Suppose that there is a decline in the demand for wheat. The new demand is Q=A -2P where 0
i.Will the market price be higher, equal or lower than in part b?
ii.Will each active firm produce more, the same quantity or less than in part b?
iii.Will the total market quantity be higher, equal or lower than that in part b?
iv.Will there be more active firms, the same number of active firms or fewer active firms compared with part b?
2.Consider the cost function C(q)=20q+F if q>0 and C(0)=0. Where F>0.
a.Find the marginal cost of production.
b.Find the average cost of production.
c.Are there economies or dis-economies of scale with this production function?
d.Explain why if technology is such that this is the cost of production, we would not expect the market to be perfectly competitive.
e.Suppose demand is p=100-2Q. A social planner, could choose any price, quantity and number of firms for this market. The planner is guided by two principles: 1. Choose total quantity Q that results in efficiently allocation.2. Minimize the total cost of producing Q. What quantity should the planner choose for this market? How many firms would you choose to produce this total quantity?
3.(Monopoly) Consider a monopoly market. Demand is given by p=100-2Q, the monopoly has a cost function C(Q)=20Q+F if Q>0 and C(0)=0. Where F>0. [Note, in class we solved a similar problem with F=0, now we assume a fixed cost].
a.Formally write the monopoly profit maximization problem.
Assume in parts b-e that the monopoly optimally produces a positive quantity.
b. Derive the first order.
c.Find the monopoly quantity.
d. Find the monopoly price.
e.Find the monopoly profit.
f.We assumed so far that the firm produces Q>0, however, if the fixed cost is higher, the monopoly might be better off not producing. For what values of F is this profit non-negative?
g. What quantity should monopolist produce if F=850?
h. What quantity should monopolist produce if F=100?
4.Suppose there is one firm in a market with linear demand function. The firm has a constant marginal cost of $9. The firm is currently charging $15 per unit, where the elasticity of demand is 3. The new CEO of this firm suspects that the current pricing strategy of this firm might not be profit maximizing. He hires you as an economic consultant to offer advice to this firm. Base on the information given, is the firm currently maximizing profits (choosing a monopoly price and quantity)? If not, should the firm raise its price or lower its price? Explain. [Hint, use the inverse elasticity rule. You do not need to find the new price, just say if higher or lower than $15].
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