Welfare Economics

1. Consider a pure exchange economy with two commodities (x and y) and two consumers whose marginal rates of substitution are given below:

MRS¹ MRS²

= x₁

y₁

= 2x₂ + y₂

The  total  supply  of  the  two  commodities  are  fixed  at  x¯

y¯ = 50

(a) If y₂ = 48, what must y₁ be equal to?

= 100 and

(b) Use your answer from part (a) to find the unique Pareto efficient allocation in this economy when y₂ = 48.

(c) Now imagine there is a single firm that produces both goods x and y so that supply is variable. If the price of good y is P_y = 2, what price should be charged for good x to maintain Pareto effi- ciency with the allocation you found in part (b)?

2. Consider another pure exchange economy where Yeung and Taryn con- sume apples and bananas. Use the empty edgeworth box below (or on a separate sheet of paper) to answer parts (a)-(d)

(a) The supply of apples and bananas is fixed at a = 80 and b = 50. Let the x-axis represent the distribution of apples and the y-axis represent the distribution of bananas. Correctly label both axes with tick marks increasing by 10.

(b) Assuming Yeung and Taryn have standard preferences, draw their indifference curves such that a Pareto efficient allocation exists where Taryn consumes 40 apples and 20 bananas. Label this  point p₁. Be sure to include at least three ICs each.

(c) Suppose Yeung and Taryn are initially at an inefficient allocation. Label this point p₂ and depict it’s movement to a Pareto efficient allocation.

(d) Finally, draw the contract curve for this market.

3. Recall the First Fundamental Theorem of Welfare Economics. For each of the following examples of market failure (i) state which FWT condition is violated and (ii) explain how it violates said condition.

(a) Asymmetric Information

(b) Externalities

(c) Public Goods

4. Using any of the tools we’ve learned in class, show how an efficient allocation isn’t always the one that society values the most.

 Public Goods

5. What is the ”free rider problem” as it pertains to public goods? Pro- vide an example.

6. For each of the following goods, determine whether or not you would consider them to be pure public goods or private goods. Use the definition of a public good to support your answer.

(a) Spencer’s Butte

(b) Wifi/High-speed internet

(c) Basic cable television

(d) Automatic teller machines (ATMs)

7. The following figure depicts the willingness to pay for good X for both Alejandro and Kaitlin. Assume a competitive market without the presence of externalities.

(a) Suppose X is a pure public good and the efficient market allocation is Q^∗ = 2

i. What is the market price for good X?

ii. Draw a quick sketch of market demand. Be sure to label  equilibrium values.