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Partial Equilibrium Consider a market for a single commodity

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Partial Equilibrium

Consider a market for a single commodity. There is a single consumer with (inverse) demand curve 100—20g. There is a single supplier with (inverse) supply curve 10+q.

1. Find the competitive equilibrium in this market (that is, assuming the con-sumer and supplier act like price takers, even though the market is really too small for that).

2. Calculate the producer'and consumer surplus at competitive equilibrium (from1) ?

3. Now suppose ‘there is a tax of 2 per unit. Calculate the new equilibrium, consumer surplus, ‘producer surplus, government revenue, and deadweight loss (again assuming that agents act as price takers).

4. Now suppose the supplier realizes she has a monopoly, but the consumer still acts as a price-taker. What price will the supplier charge if she uses a uniform pricing strategy?

5. Finally, suppose the supplier realizes she can use a more sophisticated pricing strategy. In particular, she will use a two-part pricing strategy (as in the amusement park model where there is an “entry fee” and then a fee per ride).

Calculate the two-part tariff.

Income	P1	P2	X1	X2
2	1	1	1	1
2	2	1	¼	3/2
2	3	1	1/9	5/3
5	2	1	¼	9/2

 

1. Can this choice behavior be modeled as if a rational consumer is generating it? Explain, briefly, with reference to the Weak Axiom of Revealed Preference.

2. Can this choose behavior be modeled as if it is generated by a retional consumer with utility function  2√x1+x2.?

3. Derive the (interior) demand function for good one of a consumer with utility function. 2√x1+x2. Show your work, step by step and justify each step. Submitting a formula even if it is the correct formula will not be sufficient.

General Equilibrium °

Alice and Bob have two divisible commodities denoted typically as x and y. Alles

has 4 of x and 4 of y. Bob has 6 of z and 6 of y, “a

Alice’s preferences can be represented by the function

µA(x,y) =4√x+y)

and Bob's by

 µB(x,y) = 2√F + y.

The Pareto set (contract curve} in this economy is strange looking. [t books like the thick red line in this graphic

However: This graphic is not drawn to scale! Do not copy it? Observe only that ‘I there is a vertical line in the interior, this is the only part of the Pareto set we will analyze.

1. Where should the vertical line be placed?

2. Find 9 Walrasian equilibrium (price and quantities),

3. Suppose instead that Alice ta endowed with 8 units of x, Repeat 1 and 2. How has the relative price of X changed? “How bap welfare changes?