This is one big problem that is broken up into four parts. Please work on this yourself as much as possible. You will find that the \Puzzle Pieces” from earlier homeworks will be very useful.
1. Consider a market with three consumers: Larry, Moe, and Curley. They each have income of Y = 120.
Their utility functions are:
• Larry: U = x0:5y0:5
• Moe: U = x0:25y0:75
• Curley: U = x0:75y0:25
(a) If the price of good y is py = 10, derive the equation for the market demand curve for good x.
(b) How much will each consumer purchase if the price of good x is px = 5? Why are they different?
Does it make sense?
(c) Draw the three individual demand curves and the market demand curve on the same graph.
Indicate the quantities when px = 5.
2. Suppose there are 3 firms that produce and sell good x. Each firm has long-run production function
q = 2K0:5L0:5.
(a) If the wage rate is w = 18, the rental rate of capital is r = 2, and K is fixed in the short-run at
K = 9, derive the equation for the short-run market supply curve.
(b) How much will each firm produce if the price of good x is px = 5?
(c) Draw supply curve for one of these firms and the market supply curve on the same graph. Indicate the quantities when px = 5.
(d) What is each firm’s short-run average total cost curve?
3. Now consider the competitive market for good x.
(a) What is the short-run equilibrium price and quantity of good x? (Note that the answers will be fractions.)
(b) How much will each firm produce? What will their short-run profits be?
(c) Graph the market (demand and supply curve etc.) and the graph of one of the firms (marginal revenue \curve,” marginal cost curve, average total cost curve, profits, etc.) side-by-side. Make sure everything is labeled perfectly!
4. Now consider the long-run equilibrium.
(a) Why will there be more than 3 firms in the market in the long-run?
(b) Explain why the following constitutes a long-run equilibrium: price is px = 6, there are 5 firms, and each produces 6 units. Your answer should:
i. Describe the firm’s choice of capital and labor (using condition MRTS = −w/r ).
ii. Describe firm’s profits.
iii. Include a diagram that modifies the diagram in 3(c) for a long-run equilibrium.
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