S2W9

Elsa and Anna consume Milkshake, M, and Chocolate, C.Elsa’s function is UD = MDCD. Anna’s utility function is UJ = (M^0.5)(C^0.5). Their endowments are MD = 20, CD = 10, MJ = 10 and

CJ =30.
What are the marginal rates of substitution for each person at the endowment point? Is the

initial endowment Pareto efficient?

Belle’s father makes both wheels and chairs. At current production levels, the marginal cost of producing a wheel is £50 and the marginal cost of producing a chair is £150. What is the marginal rate of transformation from wheels to chairs in his shop?

• 1

• 2

• 3

• 1/3

We enter a world where there are 2 goods produced in the economy: Clothes and Food. Tarzan and Jane are the only two consumers. Tarzan is endowed with 3 units of clothes and 2 units of food. Jane is endowed with 3 units of food and 2 units of clothes. Tarzan and Jane have the following utility functions.

UT =CtFt UJ =(CjFj)2

Find all possible pareto efficient outcomes (the contract curve).

Now lets imagine there are competitive markets and pricing for each good.Following from thee previous question, what is the equilibrium point now and what is the price ratio?

The Little Mermaid is trying to learn about the human world. Help her fill in the blanks about welfare economics.

The invisible hand theorem, also known as the first theorem of welfare economics, states that "An BLANK1 produced by competitive markets will BLANK2 all possible gains from exchange."

The second theorem of welfare economics states that "Any allocation on the BLANK3 can be sustained as a competitive equilibrium. "

Answer explanation

BLANK 1 = EQUILIBRIUM

BLANK 2 = EXHAUST

BLANK 3 = CONTRACT CURVE

• Yes

• No

The animals of Zootopia are hoping to achieve distributive efficiency in their city.

When two commodities X and Y must be allocated among consumers, what is a necessary condition for distributive efficiency?

• all firms be price takers

• all firms minimize cost

Suppose Remy and Linguini are the only two chefs in the world, who act as a cartel and jointly own one restaurant. They can set their menu prices as a monopoly. Now, suppose that there are 2 consumers who either eat at their restaurant or buy a competitively priced composite good Y. Is the competitive equilibrium pareto efficient? Why or why not?

Answer explanation

No. They aren't. Recall that our competitive equilibrium condition required the ratio of marginal costs to equal the MRS which equaled the price ratio. Now, however, we no longer have price is equal to marginal cost -- There is a markup! Thus, we don't get the same equilibrium which we know was pareto efficient.

If the economy of Disneyland is at point B in the graph, the input mix is:

• Pareto-efficient, so a movement to any other point would be Pareto inefficient.

• Any point along the contract curve in an Edgeworth box corresponds to a point on the
  production possibilities frontier (PPF).

• If the marginal cost of producing Good Y = 2 and the marginal cost of producing Good X
  = 1, then the MRT = 2.

• In a competitive market, the MRT is equal to the equilibrium product price ratio.

Say that there are 2 individuals who find watching Snow White and Aladdin to be perfect
compliments and have the same utility functions. What does their contract curve look like?